Advanced Search

MaplePrimes Questions

Error,(in solve)cannot solve expressions with sum(...

Asked by: ParmidaEf 5
solve sum incomplete-question
May 02 2025
1  1

Error,(in solve)cannot solve expressions with sum(f[ij]*(H[j]*gamma[j] - PS[j]*alpha[j]),j =1 .. N) for H[j]
can any one what can I do for this error?

Older posts missing images...

Asked by: Christopher2222 6030
image deleted incomplete-question
May 02 2025
1  1

What's with some of the older posts missing images?  Were they deleted by maplesoft to save space on mapleprimes servers?  (Storage is pretty cheap these days)

I actually replaced some images a while ago, maybe a few years back.  However I've come across the post again and the image is gone ... strange.  Maybe there's an AI at work here clearing out images. 

In some cases the images are just the output of Maple code plots.  That's ok to remove, I guess, but in others, people have used screenshots which contain code that have been removed where in some cases after they're removed make the entire thread useless.  It's not often but it occurs. 

Anyways, does mapleprimes sometimes clear out images?  Or is it an inadvertent effect when some maintenance is performed?

keeping n>0 same and not 0<n ?...

Asked by: nm 11353
inequality latex
May 01 2025
1  1

For compution this is not important, for latex, I find  n>0 little more clear to read than 0<n 

Is there a way to tell Maple not to reverse terms on each side of the > just for latex purposes?

It seems Maple does this only for   > and not for  <

I know the latex output follows what is displayed on the screen in Maple. And that is what happens also for display. Maple rewrites n>0 as   0<n.   

I tried changing display->Typesetting level from extended to maple standard but this had no effect. 

Is there a trick to make Maple not all the > to  <  ?

Again, I wanted to do this just for the latex output because for computation and for screen display in worksheet, it is not an the issue for me, as I only use Latex output.

It seems Maple like to make everything  based on "<" internally and that is why it reverses it?

> 

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

> 

restart;
> 

latex(n>0,'output'='string'); #why this is reverse on output?

"0<n"

> 

latex(n>m,'output'='string'); #why this is reverse on output?

"m <n"

> 

latex(n<0,'output'='string'); #but this stays the same

"n <0"

> 

latex(n<m,'output'='string'); #but this stays the same

"n <m"

> 

n>0

0 < n

 

 

Download why_reverses_may_1_2025.mw

ODE Test Fails for Solution...

Asked by: salim-barzani 1550
ode differential-equations odetest
May 01 2025
2  6

I’m trying to verify a solution given in the form from  using Maple's odeTest. Even though the paper claims the solution satisfies the ODE, Maple does not simplify the result to zero. Could someone explain why the test fails or suggest the correct way to verify it in Maple?

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

with(Physics)
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

_local(gamma)

Warning, A new binding for the name `gamma` has been created. The global instance of this name is still accessible using the :- prefix, :-`gamma`.  See ?protect for details.

  
> 

declare(u(x, t)); declare(U(xi)); declare(u(x, y, z, t)); declare(Q(xi)); declare(V(xi))

u(x, t)*`will now be displayed as`*u

  

U(xi)*`will now be displayed as`*U

  

u(x, y, z, t)*`will now be displayed as`*u

  

Q(xi)*`will now be displayed as`*Q

  

V(xi)*`will now be displayed as`*V

 (2)
> 

NULL
> 

ode := diff(G(xi), xi) = G(xi)*sqrt(A+B*G(xi)^2)

diff(G(xi), xi) = G(xi)*(A+B*G(xi)^2)^(1/2)

 (3)
> 

S1 := G(xi) = -sqrt(A/B)*csch(sqrt(A)*(xi+xi[0]))

G(xi) = -(A/B)^(1/2)*csch(A^(1/2)*(xi+xi[0]))

 (4)
> 

res := simplify(odetest(S1, ode))

(A/B)^(1/2)*csch(A^(1/2)*(xi+xi[0]))*(A^(1/2)*coth(A^(1/2)*(xi+xi[0]))+(A*coth(A^(1/2)*(xi+xi[0]))^2)^(1/2))

 (5)
> 

S2 := G(xi) = sqrt(-A/B)*sec(sqrt(-A)*(xi+xi[0]))

G(xi) = (-A/B)^(1/2)*sec((-A)^(1/2)*(xi+xi[0]))

 (6)
> 

res := simplify(odetest(S2, ode))

(-A/B)^(1/2)*sec((-A)^(1/2)*(xi+xi[0]))*((-A)^(1/2)*tan((-A)^(1/2)*(xi+xi[0]))-(-A*tan((-A)^(1/2)*(xi+xi[0]))^2)^(1/2))

 (7)
> 

S3 := G(xi) = sqrt(-A/B)*sech(sqrt(A)*(xi+xi[0]))

G(xi) = (-A/B)^(1/2)*sech(A^(1/2)*(xi+xi[0]))

 (8)
> 

res := simplify(odetest(S3, ode))

(-A^(1/2)*tanh(A^(1/2)*(xi+xi[0]))-(A*tanh(A^(1/2)*(xi+xi[0]))^2)^(1/2))*(-A/B)^(1/2)*sech(A^(1/2)*(xi+xi[0]))

 (9)
> 

S4 := G(xi) = sqrt(-A/B)*csc(sqrt(-A)*(xi+xi[0]))

G(xi) = (-A/B)^(1/2)*csc((-A)^(1/2)*(xi+xi[0]))

 (10)
> 

res := simplify(odetest(S4, ode))

(-(-A)^(1/2)*cot((-A)^(1/2)*(xi+xi[0]))-(-A*cot((-A)^(1/2)*(xi+xi[0]))^2)^(1/2))*(-A/B)^(1/2)*csc((-A)^(1/2)*(xi+xi[0]))

 (11)
> 

S5 := G(xi) = cos(sqrt(-A)*(xi+xi[0]))+sin(sqrt(-A)*(xi+xi[0]))

G(xi) = cos((-A)^(1/2)*(xi+xi[0]))+sin((-A)^(1/2)*(xi+xi[0]))

 (12)
> 

res := simplify(odetest(S5, ode))

(cos((-A)^(1/2)*(xi+xi[0]))-sin((-A)^(1/2)*(xi+xi[0])))*(-A)^(1/2)+(B*sin(2*(-A)^(1/2)*(xi+xi[0]))+A+B)^(1/2)*(-cos((-A)^(1/2)*(xi+xi[0]))-sin((-A)^(1/2)*(xi+xi[0])))

 (13)
> 

S6 := G(xi) = 1/(sqrt(B)*(xi+xi[0]))

G(xi) = 1/(B^(1/2)*(xi+xi[0]))

 (14)
> 

odetest(S6, subs(A = 0, ode))

-csgn(1/(xi+xi[0]))/(B^(1/2)*(xi+xi[0])^2)-1/(B^(1/2)*(xi+xi[0])^2)

 (15)
> 

S7 := G(xi) = 1/(sqrt(-B)*(xi+xi[0]))

G(xi) = 1/((-B)^(1/2)*(xi+xi[0]))

 (16)
> 

odetest(S7, subs(A = 0, ode))

-(-1/(xi+xi[0])^2)^(1/2)*xi[0]/((-B)^(1/2)*(xi+xi[0])^2)-(-1/(xi+xi[0])^2)^(1/2)*xi/((-B)^(1/2)*(xi+xi[0])^2)-1/((-B)^(1/2)*(xi+xi[0])^2)

 (17)
> 

ode2 := diff(G(xi), xi) = A+B*G(xi)^2

diff(G(xi), xi) = A+B*G(xi)^2

 (18)
> 

S8 := G(xi) = sgn(A)*sqrt(A/B)*tan(sqrt(A*B)*(xi+xi[0]))

G(xi) = sgn(A)*(A/B)^(1/2)*tan((A*B)^(1/2)*(xi+xi[0]))

 (19)
> 

res := simplify(odetest(S8, ode2))

(sgn(A)*(A*B)^(1/2)*(tan((A*B)^(1/2)*xi[0])^2+1)*(tan((A*B)^(1/2)*xi)^2+1)*(A/B)^(1/2)-A*((tan((A*B)^(1/2)*xi)+tan((A*B)^(1/2)*xi[0]))^2*sgn(A)^2+(tan((A*B)^(1/2)*xi[0])*tan((A*B)^(1/2)*xi)-1)^2))/(tan((A*B)^(1/2)*xi[0])*tan((A*B)^(1/2)*xi)-1)^2

 (20)
> 

NULL
> 

S9 := G(xi) = -sgn(A)*sqrt(A/B)*cot(sqrt(A*B)*(xi+xi[0]))

G(xi) = -sgn(A)*(A/B)^(1/2)*cot((A*B)^(1/2)*(xi+xi[0]))

 (21)
> 

res := simplify(odetest(S9, ode2))

(sgn(A)*(A*B)^(1/2)*(cot((A*B)^(1/2)*xi[0])^2+1)*(cot((A*B)^(1/2)*xi)^2+1)*(A/B)^(1/2)-A*((cot((A*B)^(1/2)*xi[0])*cot((A*B)^(1/2)*xi)-1)^2*sgn(A)^2+(cot((A*B)^(1/2)*xi[0])+cot((A*B)^(1/2)*xi))^2))/(cot((A*B)^(1/2)*xi[0])+cot((A*B)^(1/2)*xi))^2

 (22)
> 

NULL
> 

S9 := G(xi) = sgn(A)*sqrt(-A/B)*tanh(sqrt(-A*B)*(xi+xi[0]))

G(xi) = sgn(A)*(-A/B)^(1/2)*tanh((-A*B)^(1/2)*(xi+xi[0]))

 (23)
> 

res := simplify(odetest(S9, ode2))

(A*(sgn(A)^2-1)*cosh(2*(-A*B)^(1/2)*(xi+xi[0]))-sgn(A)^2*A+2*sgn(A)*(-A/B)^(1/2)*(-A*B)^(1/2)-A)/(1+cosh(2*(-A*B)^(1/2)*(xi+xi[0])))

 (24)
> 

NULL
> 

S10 := G(xi) = sgn(A)*sqrt(-A/B)*coth(sqrt(-A*B)*(xi+xi[0]))

G(xi) = sgn(A)*(-A/B)^(1/2)*coth((-A*B)^(1/2)*(xi+xi[0]))

 (25)
> 

odetest(S10, ode2)

(sgn(A)^2*A*cosh(2*(-A*B)^(1/2)*(xi+xi[0]))+sgn(A)^2*A-2*sgn(A)*(-A/B)^(1/2)*(-A*B)^(1/2)-A*cosh(2*(-A*B)^(1/2)*(xi+xi[0]))+A)/(-1+cosh(2*(-A*B)^(1/2)*(xi+xi[0])))

 (26)
> 

NULL
> 

S11 := G(xi) = -1/(B*(xi+xi[0]))

G(xi) = -1/(B*(xi+xi[0]))

 (27)
> 

odetest(S11, subs(A = 0, ode2))

0

 (28)
> 

S12 := G(xi) = A*(xi+xi[0])

G(xi) = A*(xi+xi[0])

 (29)
> 

odetest(S12, subs(B = 0, ode2))

0

 (30)

Download Z1.mw

ODE odetest not returning zero – possible mistake?...

Asked by: salim-barzani 1550
ode assumptions differential-equations
May 01 2025
3  2

Why doesn't this ODE return zero when using odetest? Did I do something wrong?

Would you like help checking the equation or debugging the issue?

> 

restart
> 

with(PDEtools)
> 

declare(P(mu))

P(mu)*`will now be displayed as`*P

 (1)
> 

assume(A::real, r::real, rho::real, lambda::real)
> 

Psol := P(mu) = 2*A*lambda/((A^2+r)*exp(lambda*rho*mu)+r*exp(-lambda*rho*mu))

P(mu) = 2*A*lambda/((A^2+r)*exp(lambda*rho*mu)+r*exp(-lambda*rho*mu))

 (2)
> 

ode := (diff(P(mu), mu))^2-rho^2*P(mu)^2*(1+r*P(mu)^2) = 0

(diff(P(mu), mu))^2-rho^2*P(mu)^2*(1+r*P(mu)^2) = 0

 (3)
> 

res := odetest(Psol, ode)

4*A^6*rho^2*lambda^4*exp(6*lambda*rho*mu)/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4+8*r*A^4*rho^2*lambda^4*exp(6*lambda*rho*mu)/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4-24*A^4*lambda^4*rho^2*exp(4*lambda*rho*mu)*r/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4-4*A^6*rho^2*lambda^2*exp(6*lambda*rho*mu)/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4+4*A^2*r^2*rho^2*lambda^4*exp(6*lambda*rho*mu)/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4-8*A^2*lambda^4*rho^2*exp(4*lambda*rho*mu)*r^2/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4+4*A^2*r^2*rho^2*lambda^4*exp(2*lambda*rho*mu)/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4-8*r*A^4*rho^2*lambda^2*exp(6*lambda*rho*mu)/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4-8*A^4*lambda^2*rho^2*exp(4*lambda*rho*mu)*r/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4-4*A^2*r^2*rho^2*lambda^2*exp(6*lambda*rho*mu)/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4-8*A^2*lambda^2*rho^2*exp(4*lambda*rho*mu)*r^2/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4-4*A^2*r^2*rho^2*lambda^2*exp(2*lambda*rho*mu)/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4

 (4)
> 

simplify(res)

4*lambda^2*exp(2*lambda*rho*mu)*(((-2*lambda^2-2)*r^2+(-6*lambda^2-2)*A^2*r)*exp(2*lambda*rho*mu)+(lambda+1)*((A^2+r)^2*exp(4*lambda*rho*mu)+r^2)*(lambda-1))*A^2*rho^2/((A^2+r)*exp(2*lambda*rho*mu)+r)^4

 (5)
> 

P_hyper := P(mu) = 2*A*lambda/((A^2+r)*cosh(rho*mu)+(A^2-r)*sinh(rho*mu))

P(mu) = 2*A*lambda/((A^2+r)*cosh(rho*mu)+(A^2-r)*sinh(rho*mu))

 (6)
> 

res_hyper := simplify(odetest(P_hyper, ode), symbolic)

-16*A^4*lambda^2*rho^2*r*(lambda^2+1)/((A^2+r)*cosh(rho*mu)+(A^2-r)*sinh(rho*mu))^4

 (7)
 

NULL

Download ode.mw

why some help pages are empty?...

Asked by: nm 11353
documentation
May 01 2025
3  1

This happens in Maple 2025, but when I checked Maple 2024.2, same thing happen.

To reproduce, I typed ?coeff in the worksheet. Now the help page for coeff comes up OK. On the right, there are some links below "see also". 

Clicking on the one that says PolynomialTools[CoefficientVector] and now an EMPTY page opens up.

Also, typing ?PolynomialTools in worksheet, opens the help page for Overview of the PolynomialTools Package. Now clicking on CoefficientList link, opens an EMPTY page. Same when clicking on CoefficientVector, an EMPTY page !

Have not checked all the links in the help page, but why are some commands have empty help pages?

 

 

Does Maple provide bold notation for vectors...

Asked by: C_R 3372
typesetting vector
May 01 2025
2  17

I am interested in having bold notation for vectors and matrices.

Any commands or packages that output expressions this way?

Verifying ODE Solution and Issues with Assumptions...

Asked by: salim-barzani 1550
ode assumptions differential-equations
April 30 2025
3  2

I’m trying to test a specific function as a solution to a nonlinear ODE in Maple. The equation is of the Riccati type, and my candidate solution involves parameters A, B, and C.

I've used assuming to specify the condition (4AC−B2)>0 and (4AC - B^2) <0, but when I use odetest to verify the solution, I still get a nonzero result. Additionally, when I apply the assumption, Maple sometimes introduces a negation sign in the output (e.g., changing sqrt(...) into -sqrt(...)), which wasn't part of the original solution.

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

with(Physics)
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

E := diff(G(xi), xi) = A+B*G(xi)+C*G(xi)^2

diff(G(xi), xi) = A+B*G(xi)+C*G(xi)^2

 (2)
> 

> 

S1 := G(xi) = (sqrt(4*A*C-B^2)*tan((1/2)*sqrt(4*A*C-B^2)*(d[0]+xi))-B)/(2*C)

G(xi) = (1/2)*((4*A*C-B^2)^(1/2)*tan((1/2)*(4*A*C-B^2)^(1/2)*(d[0]+xi))-B)/C

 (3)
> 

odetest(S1, E)

0

 (4)
> 

> 

S2 := G(xi) = -(sqrt(4*A*C-B^2)*cot((1/2)*sqrt(4*A*C-B^2)*(d[0]+xi))+B)/(2*C)

G(xi) = -(1/2)*((4*A*C-B^2)^(1/2)*cot((1/2)*(4*A*C-B^2)^(1/2)*(d[0]+xi))+B)/C

 (5)
> 

odetest(S2, E)

0

 (6)
> 

assume(4*A*C-B^2 < 0)
> 

S3 := G(xi) = -(sqrt(4*A*C-B^2)*tanh((1/2)*sqrt(4*A*C-B^2)*(d[0]+xi))+B)/(2*C)

G(xi) = -(1/2)*((4*A*C-B^2)^(1/2)*tanh((1/2)*(4*A*C-B^2)^(1/2)*(d[0]+xi))+B)/C

 (7)
> 

odetest(S3, E)

-2*A+(1/2)*B^2/C

 (8)

Download A2.mw

Why the subs command not apply ?...

Asked by: salim-barzani 1550
radical substitution subs
April 29 2025
3  9

i did every thing coreectly but nothing happen not apply where is my mistake?

> 

``
> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

with(Physics)
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

NULL
> 

S := (diff(G(xi), xi))^2-r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2) = 0

(diff(G(xi), xi))^2-r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2) = 0

 (2)
> 

SS := diff(G(xi), xi) = sqrt(r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2))

diff(G(xi), xi) = (r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2))^(1/2)

 (3)
> 

Se := sqrt(r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2)) = diff(G(xi), xi)

(r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2))^(1/2) = diff(G(xi), xi)

 (4)
> 

dub := diff(SS, xi)

diff(diff(G(xi), xi), xi) = (1/2)*(2*r^2*G(xi)*(a+b*G(xi)+l*G(xi)^2)*(diff(G(xi), xi))+r^2*G(xi)^2*(b*(diff(G(xi), xi))+2*l*G(xi)*(diff(G(xi), xi))))/(r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2))^(1/2)

 (5)
> 

Dubl2 := simplify(diff(diff(G(xi), xi), xi) = (1/2)*(2*r^2*G(xi)*(a+b*G(xi)+l*G(xi)^2)*(diff(G(xi), xi))+r^2*G(xi)^2*(b*(diff(G(xi), xi))+2*l*G(xi)*(diff(G(xi), xi))))/(r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2))^(1/2))

diff(diff(G(xi), xi), xi) = (1/2)*r^2*G(xi)*(diff(G(xi), xi))*(4*l*G(xi)^2+3*b*G(xi)+2*a)/(r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2))^(1/2)

 (6)
> 

subs(SA, Dubl2)

diff((r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2))^(1/2), xi) = (1/2)*r^2*G(xi)*(4*l*G(xi)^2+3*b*G(xi)+2*a)

 (7)
> 

subs(Se, Dubl2)

diff(diff(G(xi), xi), xi) = (1/2)*r^2*G(xi)*(diff(G(xi), xi))*(4*l*G(xi)^2+3*b*G(xi)+2*a)/(r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2))^(1/2)

 (8)
> 

subs(lhs(Se) = rhs(Se), Dubl2)

diff(diff(G(xi), xi), xi) = (1/2)*r^2*G(xi)*(diff(G(xi), xi))*(4*l*G(xi)^2+3*b*G(xi)+2*a)/(r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2))^(1/2)

 (9)
 

NULL

Download subs.mw

Computing the left and right eigenvectors...

Asked by: Elisha 50
eigenvector
April 29 2025
2  1

Someone please help me with the computation of the right and left eigenvectors. my system of equation is attached below

> 

with(VectorCalculus):
 
> 

interface(imaginaryunit = I)

I

 (2)
> 

I

I

 (3)
> 

sqrt(-4)

2*I

 (4)
> 

NULL
> 

``

Limit(N(t) = N__0*exp(-mu*t)+exp(mu*t)*K/mu, t = infinity)

  

limit(N(t), t = infinity) = limit(N__0*exp(-mu*t)+exp(mu*t)*K/mu, t = infinity)

 (5)
> 

 

> 

NULL
> 

#to calculate the  disease free equilibrium,
> 

NULL
> 

E1 := -S*µ__C+`&Lambda;__p`

-S*µ__C+Lambda__p

 (6)
> 

NULL

``

 (7)
> 

E3 := -S__A*µ__A+`&Lambda;__A`

-S__A*µ__A+Lambda__A

 (8)
> 

NULL

``

 (9)
> 

NULL

``

 (10)
> 

NULL
> 

solve({E1 = 0, E3 = 0}, {S, S__A})

{S = Lambda__p/µ__C, S__A = Lambda__A/µ__A}

 (11)
> 

NULL
> 

NULL#to calculate the Endemic Equilibrium state,

Typesetting:-mparsed()

 (12)
> 

restart
> 

with(VectorCalculus):
 
> 

interface(imaginaryunit = I)

I

 (14)
> 

I

I

 (15)
> 

sqrt(-4)

2*I

 (16)
> 

``
> 

E1 := `&Lambda;__p`-(`&varphi;`*`&theta;__B`*I__A/N__p+µ__C)*S+`&omega;__B`*I__B

Lambda__p-(varphi*theta__B*I__A/N__p+µ__C)*S+omega__B*I__B

 (17)
> 

E2 := `&varphi;`*`&theta;__B`*I__A*S/N__p-`&omega;__B`*I__B-(`&sigma;__B`+µ__C)*I__B

varphi*theta__B*I__A*S/N__p-omega__B*I__B-(sigma__B+µ__C)*I__B

 (18)

``

 (19)
> 

E3 := `&Lambda;__A`-(µ__A+`&varphi;`*`&alpha;__B`*I__B/N__p)*S__A+`&delta;__A`*I__A

Lambda__A-(µ__A+varphi*alpha__B*I__B/N__p)*S__A+delta__A*I__A

 (20)
> 

E4 := `&varphi;`*`&alpha;__B`*I__B*S__A/N__p-(µ__A+`&delta;__A`)*I__A

varphi*alpha__B*I__B*S__A/N__p-(µ__A+delta__A)*I__A

 (21)
> 

NULL

``

 (22)
> 

NULL

``

 (23)
> 

solve({E1 = 0, E2 = 0, E3 = 0, E4 = 0}, {I__A, I__B, S, S__A})

{I__A = 0, I__B = 0, S = Lambda__p/µ__C, S__A = Lambda__A/µ__A}, {I__A = -(N__p^2*µ__A^2*µ__C^2+N__p^2*µ__A^2*µ__C*omega__B+N__p^2*µ__A^2*µ__C*sigma__B+N__p^2*µ__A*µ__C^2*delta__A+N__p^2*µ__A*µ__C*delta__A*omega__B+N__p^2*µ__A*µ__C*delta__A*sigma__B-varphi^2*Lambda__A*Lambda__p*alpha__B*theta__B)/(varphi*µ__A*theta__B*(N__p*µ__A*µ__C+N__p*µ__A*sigma__B+N__p*µ__C*delta__A+N__p*delta__A*sigma__B+varphi*Lambda__p*alpha__B)), I__B = -(N__p^2*µ__A^2*µ__C^2+N__p^2*µ__A^2*µ__C*omega__B+N__p^2*µ__A^2*µ__C*sigma__B+N__p^2*µ__A*µ__C^2*delta__A+N__p^2*µ__A*µ__C*delta__A*omega__B+N__p^2*µ__A*µ__C*delta__A*sigma__B-varphi^2*Lambda__A*Lambda__p*alpha__B*theta__B)/(alpha__B*(N__p*µ__A*µ__C^2+N__p*µ__A*µ__C*omega__B+N__p*µ__A*µ__C*sigma__B+varphi*µ__C*Lambda__A*theta__B+varphi*Lambda__A*sigma__B*theta__B)*varphi), S = (N__p*µ__A*µ__C+N__p*µ__A*sigma__B+N__p*µ__C*delta__A+N__p*delta__A*sigma__B+varphi*Lambda__p*alpha__B)*µ__A*N__p*(µ__C+omega__B+sigma__B)/(alpha__B*varphi*(N__p*µ__A*µ__C^2+N__p*µ__A*µ__C*omega__B+N__p*µ__A*µ__C*sigma__B+varphi*µ__C*Lambda__A*theta__B+varphi*Lambda__A*sigma__B*theta__B)), S__A = N__p*(N__p*µ__A^2*µ__C^2+N__p*µ__A^2*µ__C*omega__B+N__p*µ__A^2*µ__C*sigma__B+N__p*µ__A*µ__C^2*delta__A+N__p*µ__A*µ__C*delta__A*omega__B+N__p*µ__A*µ__C*delta__A*sigma__B+varphi*µ__A*µ__C*Lambda__A*theta__B+varphi*µ__A*Lambda__A*sigma__B*theta__B+varphi*µ__C*Lambda__A*delta__A*theta__B+varphi*Lambda__A*delta__A*sigma__B*theta__B)/(varphi*µ__A*theta__B*(N__p*µ__A*µ__C+N__p*µ__A*sigma__B+N__p*µ__C*delta__A+N__p*delta__A*sigma__B+varphi*Lambda__p*alpha__B))}

 (24)
> 

``

J := Jacobian([E1, E2, E3, E4], [S, I__B, S__A, I__A])

Matrix(%id = 18446746854857131062)

 (25)

NULL

> 

restart
> 

J := Matrix(4, 4, {(1, 1) = -`&varphi;`*`&theta;__B`*I__A/N__p-µ__C, (1, 2) = `&omega;__B`, (1, 3) = 0, (1, 4) = -`&varphi;`*`&theta;__B`*S/N__p, (2, 1) = `&varphi;`*`&theta;__B`*I__A/N__p, (2, 2) = -`&omega;__B`-`&sigma;__B`-µ__C, (2, 3) = 0, (2, 4) = `&varphi;`*`&theta;__B`*S/N__p, (3, 1) = 0, (3, 2) = -`&varphi;`*`&alpha;__B`*S__A/N__p, (3, 3) = -µ__A-`&varphi;`*`&alpha;__B`*I__B/N__p, (3, 4) = `&delta;__A`, (4, 1) = 0, (4, 2) = `&varphi;`*`&alpha;__B`*S__A/N__p, (4, 3) = `&varphi;`*`&alpha;__B`*I__B/N__p, (4, 4) = -µ__A-`&delta;__A`})

Matrix(%id = 18446746579340105118)

 (26)

S := `&Lambda;__p`/µ__C

Lambda__p/µ__C

 (27)

S__A := `&Lambda;__A`/µ__A

Lambda__A/µ__A

 (28)

I__B := 0

0

 (29)

I__A := 0

0

 (30)

NULL

0

 (31)

J := Matrix(4, 4, {(1, 1) = -`&varphi;`*`&theta;__B`*I__A/N__p-µ__C, (1, 2) = `&omega;__B`, (1, 3) = 0, (1, 4) = -`&varphi;`*`&theta;__B`*S/N__p, (2, 1) = `&varphi;`*`&theta;__B`*I__A/N__p, (2, 2) = -`&omega;__B`-`&sigma;__B`-µ__C, (2, 3) = 0, (2, 4) = `&varphi;`*`&theta;__B`*S/N__p, (3, 1) = 0, (3, 2) = -`&varphi;`*`&alpha;__B`*S__A/N__p, (3, 3) = -µ__A-`&varphi;`*`&alpha;__B`*I__B/N__p, (3, 4) = `&delta;__A`, (4, 1) = 0, (4, 2) = `&varphi;`*`&alpha;__B`*S__A/N__p, (4, 3) = `&varphi;`*`&alpha;__B`*I__B/N__p, (4, 4) = -µ__A-`&delta;__A`})

Matrix(%id = 18446746579340107518)

 (32)
> 

J := Matrix(4, 4, {(1, 1) = -µ__C, (1, 2) = `&omega;__B`, (1, 3) = 0, (1, 4) = -`&beta;__1`, (2, 1) = 0, (2, 2) = -`&omega;__B`-`&sigma;__B`-µ__C, (2, 3) = 0, (2, 4) = -`&beta;__1`, (3, 1) = 0, (3, 2) = -`&beta;__2`, (3, 3) = -µ__A, (3, 4) = `&delta;__A`, (4, 1) = 0, (4, 2) = `&beta;__2`, (4, 3) = 0, (4, 4) = -µ__A-`&delta;__A`})

Matrix(%id = 18446746579417403630)

 (33)
> 

"simplify( ? )"

Matrix(%id = 18446746579305905318)

 (34)
> 

"LinearAlgebra:-Eigenvalues( ? )"

Vector[column](%id = 18446746579445964182)

 (35)
> 

"LinearAlgebra:-CharacteristicPolynomial( ?, lambda )"

lambda^4+(2*µ__A+delta__A+omega__B+sigma__B+2*µ__C)*lambda^3+(beta__1*beta__2+µ__A^2+4*µ__A*µ__C+µ__A*delta__A+2*µ__A*omega__B+2*µ__A*sigma__B+µ__C^2+2*µ__C*delta__A+µ__C*omega__B+µ__C*sigma__B+delta__A*omega__B+delta__A*sigma__B)*lambda^2+(beta__1*beta__2*µ__A+beta__1*beta__2*µ__C+2*µ__A^2*µ__C+µ__A^2*omega__B+µ__A^2*sigma__B+2*µ__A*µ__C^2+2*µ__A*µ__C*delta__A+2*µ__A*µ__C*omega__B+2*µ__A*µ__C*sigma__B+µ__A*delta__A*omega__B+µ__A*delta__A*sigma__B+µ__C^2*delta__A+µ__C*delta__A*omega__B+µ__C*delta__A*sigma__B)*lambda+beta__1*beta__2*µ__A*µ__C+µ__A^2*µ__C^2+µ__A^2*µ__C*omega__B+µ__A^2*µ__C*sigma__B+µ__A*µ__C^2*delta__A+µ__A*µ__C*delta__A*omega__B+µ__A*µ__C*delta__A*sigma__B

 (36)
> 

NULL

"(->)"

Vector[column](%id = 18446746579340117046)

 (37)

# to find the trace we

 

Matrix(7, 7, {(1, 1) = -beta*lambda-v__1-µ, (1, 2) = v__2, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0, (2, 1) = v__1, (2, 2) = beta*(w-1)*lambda-µ-v__2-alpha, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (2, 7) = 0, (3, 1) = 0, (3, 2) = alpha, (3, 3) = -µ, (3, 4) = 0, (3, 5) = `&rho;__A`, (3, 6) = `&rho;__F`, (3, 7) = -(-1+k)*`&rho;__Q`, (4, 1) = beta*lambda, (4, 2) = -beta*(w-1)*lambda, (4, 3) = 0, (4, 4) = -q__E-delta-µ, (4, 5) = 0, (4, 6) = 0, (4, 7) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = a*delta, (5, 5) = -`&rho;__A`-q__A-µ, (5, 6) = 0, (5, 7) = k*`&rho;__Q`, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = -delta*(-1+a), (6, 5) = 0, (6, 6) = -`&rho;__F`-q__F-`&delta;__F`-µ, (6, 7) = 0, (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = q__E, (7, 5) = q__A, (7, 6) = q__F, (7, 7) = -`&rho;__Q`-`&delta;__Q`-µ})

Matrix(%id = 36893490965935089652)

 (38)

"(->)"

-beta*lambda-v__1-7*µ+beta*(w-1)*lambda-v__2-alpha-q__E-delta-rho__A-q__A-rho__F-q__F-delta__F-rho__Q-delta__Q

 (39)

 

#this shows that trace is negative

 

#to Achieve stability, the value below must be less than zero

 

(-q__E-delta-µ)*(-`&rho;__F`-q__F-`&delta;__F`-µ)*(-k*q__A*`&rho;__Q`+q__A*µ+q__A*`&delta;__Q`+q__A*`&rho;__Q`+µ^2+µ*`&delta;__Q`+µ*`&rho;__A`+µ*`&rho;__Q`+`&delta;__Q`*`&rho;__A`+`&rho;__A`*`&rho;__Q`)*µ < 0

(-q__E-delta-µ)*(-rho__F-q__F-delta__F-µ)*(-k*q__A*rho__Q+q__A*rho__Q+q__A*µ+q__A*delta__Q+rho__A*rho__Q+rho__A*µ+rho__A*delta__Q+rho__Q*µ+µ^2+µ*delta__Q)*µ < 0

 (40)

 NULL

> 

M := diff(N(t), t) = Pi-µ*N(t)

diff(N(t), t) = Pi-µ*N(t)

 (41)
> 

dsolve({M}, N(t))

{N(t) = Pi/µ+exp(-µ*t)*_C1}

 (42)
> 

eval({N(t) = Pi/µ+exp(-µ*t)*_C1}, [t = infinity])

{N(infinity) = Pi/µ+exp(-µ*infinity)*_C1}

 (43)
> 

value(%)

{N(infinity) = Pi/µ+exp(-µ*infinity)*_C1}

 (44)
> 

Limit(N(t) = Pi/µ+exp(-µ*t)*_C1, t = infinity); value(%)

Limit(N(t) = Pi/µ+exp(-µ*t)*_C1, t = infinity)

  

limit(N(t), t = infinity) = limit(Pi/µ+exp(-µ*t)*_C1, t = infinity)

 (45)

 

> 

Subs := diff(S(t), t) = -(beta*lambda+v__1+µ)*S(t)

diff(S(t), t) = -(beta*lambda+v__1+µ)*S(t)

 (46)
> 

dsolve({Subs}, S(t))

{S(t) = _C1*exp(-(beta*lambda+v__1+µ)*t)}

 (47)
 

``

Download Cotton_DFE_and_Jacobian.mw

Help with Solving ODE and Representing ± Sign...

Asked by: salim-barzani 1550
ode dsolve differential-equations
April 29 2025
3  8

I tried solving this ODE, but my result is very different from the expected one. How can I correctly obtain the solution? Also, is there a way to include both the positive and negative signs (±) in the equation so that the final result reflects both possibilities?

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

with(Physics)
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

_local(gamma)

Warning, A new binding for the name `gamma` has been created. The global instance of this name is still accessible using the :- prefix, :-`gamma`.  See ?protect for details.

  
> 

declare(Omega(x, t)); declare(U(xi)); declare(u(x, y, z, t)); declare(Q(xi)); declare(V(xi))

Omega(x, t)*`will now be displayed as`*Omega

  

U(xi)*`will now be displayed as`*U

  

u(x, y, z, t)*`will now be displayed as`*u

  

Q(xi)*`will now be displayed as`*Q

  

V(xi)*`will now be displayed as`*V

 (2)
> 

``
> 

ode := f*g^3*(diff(diff(U(xi), xi), xi))-4*f*p*U(xi)-6*k*l*U(xi)-f^3*g*(diff(diff(U(xi), xi), xi))+6*f*g*U(xi)^2 = 0

f*g^3*(diff(diff(U(xi), xi), xi))-4*f*p*U(xi)-6*k*l*U(xi)-f^3*g*(diff(diff(U(xi), xi), xi))+6*f*g*U(xi)^2 = 0

 (3)
> 

S := (diff(G(xi), xi))^2-r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2) = 0

(diff(G(xi), xi))^2-r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2) = 0

 (4)
> 

S1 := dsolve(S, G(xi))

G(xi) = (1/2)*(-b+(-4*a*l+b^2)^(1/2))/l, G(xi) = -(1/2)*(b+(-4*a*l+b^2)^(1/2))/l, G(xi) = -4*a*exp(c__1*r*a^(1/2))/(exp(xi*r*a^(1/2))*(4*a*l-b^2+2*b*exp(c__1*r*a^(1/2))/exp(xi*r*a^(1/2))-(exp(c__1*r*a^(1/2)))^2/(exp(xi*r*a^(1/2)))^2)), G(xi) = -4*a*exp(xi*r*a^(1/2))/(exp(c__1*r*a^(1/2))*(4*a*l-b^2+2*b*exp(xi*r*a^(1/2))/exp(c__1*r*a^(1/2))-(exp(xi*r*a^(1/2)))^2/(exp(c__1*r*a^(1/2)))^2))

 (5)
> 

S2 := S1[3]

G(xi) = -4*a*exp(c__1*r*a^(1/2))/(exp(xi*r*a^(1/2))*(4*a*l-b^2+2*b*exp(c__1*r*a^(1/2))/exp(xi*r*a^(1/2))-(exp(c__1*r*a^(1/2)))^2/(exp(xi*r*a^(1/2)))^2))

 (6)
> 

normal(G(xi) = -4*a*exp(c__1*r*a^(1/2))/(exp(xi*r*a^(1/2))*(4*a*l-b^2+2*b*exp(c__1*r*a^(1/2))/exp(xi*r*a^(1/2))-(exp(c__1*r*a^(1/2)))^2/(exp(xi*r*a^(1/2)))^2)), ':-expanded')

G(xi) = 4*a*exp(c__1*r*a^(1/2))*exp(xi*r*a^(1/2))/(-4*a*l*(exp(xi*r*a^(1/2)))^2+b^2*(exp(xi*r*a^(1/2)))^2-2*b*exp(c__1*r*a^(1/2))*exp(xi*r*a^(1/2))+(exp(c__1*r*a^(1/2)))^2)

 (7)
> 

simplify(G(xi) = 4*a*exp(c__1*r*a^(1/2))*exp(xi*r*a^(1/2))/(-4*a*l*(exp(xi*r*a^(1/2)))^2+b^2*(exp(xi*r*a^(1/2)))^2-2*b*exp(c__1*r*a^(1/2))*exp(xi*r*a^(1/2))+(exp(c__1*r*a^(1/2)))^2))

G(xi) = -4*a*exp(a^(1/2)*r*(c__1+xi))/(4*a*l*exp(2*xi*r*a^(1/2))-b^2*exp(2*xi*r*a^(1/2))+2*b*exp(a^(1/2)*r*(c__1+xi))-exp(2*c__1*r*a^(1/2)))

 (8)
> 

convert(%, trig)

G(xi) = -4*a*(cosh(a^(1/2)*r*(c__1+xi))+sinh(a^(1/2)*r*(c__1+xi)))/(4*a*l*(cosh(2*xi*r*a^(1/2))+sinh(2*xi*r*a^(1/2)))-b^2*(cosh(2*xi*r*a^(1/2))+sinh(2*xi*r*a^(1/2)))+2*b*(cosh(a^(1/2)*r*(c__1+xi))+sinh(a^(1/2)*r*(c__1+xi)))-cosh(2*c__1*r*a^(1/2))-sinh(2*c__1*r*a^(1/2)))

 (9)
> 

convert(S1[3], trig)

G(xi) = -4*a*(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))/((cosh(xi*r*a^(1/2))+sinh(xi*r*a^(1/2)))*(4*a*l-b^2+2*b*(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))/(cosh(xi*r*a^(1/2))+sinh(xi*r*a^(1/2)))-(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))^2/(cosh(xi*r*a^(1/2))+sinh(xi*r*a^(1/2)))^2))

 (10)
> 

simplify(G(xi) = -4*a*(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))/((cosh(xi*r*a^(1/2))+sinh(xi*r*a^(1/2)))*(4*a*l-b^2+2*b*(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))/(cosh(xi*r*a^(1/2))+sinh(xi*r*a^(1/2)))-(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))^2/(cosh(xi*r*a^(1/2))+sinh(xi*r*a^(1/2)))^2)))

G(xi) = -4*a*(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))*(cosh(xi*r*a^(1/2))+sinh(xi*r*a^(1/2)))/((4*a*l-b^2)*cosh(xi*r*a^(1/2))^2+((8*a*l-2*b^2)*sinh(xi*r*a^(1/2))+2*b*(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2))))*cosh(xi*r*a^(1/2))+(4*a*l-b^2)*sinh(xi*r*a^(1/2))^2+2*b*(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))*sinh(xi*r*a^(1/2))-(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))^2)

 (11)
   

Download tt.mw

Slider Plot and Value Substitution Help...

Asked by: Andiguys 65
parameters explore plotting
April 29 2025
0  4

I need to create a slider plot for A10, A11, and A12 by varying the parameters theta, Pu, and a.
I have a syntax ready — could you suggest modifications to make it work correctly and generate the plot?

Additionally, is it possible to compute the values of A13 and A14 by substituting the obtained A10, A11, and A12 values for each combination of theta, Pu, and a from the slider plot?

Sheet attached: Slider_Q.mw

bug report. dsolve sometimes gives series solution...

Asked by: nm 11353
ode series differential-equations
April 28 2025
1  3

The series to ode using 'series' option (if it exists) should always be series(...), i.e. with big O at end. but sometimes Maple forgets to add this. Here is an example

> 

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1862 and is the same as the version installed in this computer, created 2025, April 25, 10:33 hours Pacific Time.`

> 

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 15 and is the same as the version installed in this computer, created April 27, 2025, 23:18 hours Eastern Time.`

> 

restart;
> 

ode:=diff(y(x),x)+y(x)=1+x;
IC:=y(0)=0;
sol:=dsolve([ode,IC],y(x),'series')

diff(y(x), x)+y(x) = 1+x

y(0) = 0

y(x) = x

> 

lprint(sol); # notice solution is not series, it should be

y(x) = x

> 

#above solution should be
y(x) = series(x+O(x^6),x,6)

y(x) = series(x+O(x^6),x,6)

> 

#this example below is correct
ode:=diff(y(x),x)+y(x)=1+x;
IC:=y(0)=1;
sol:=dsolve([ode,IC],y(x),'series')

diff(y(x), x)+y(x) = 1+x

y(0) = 1

y(x) = series(1+(1/2)*x^2-(1/6)*x^3+(1/24)*x^4-(1/120)*x^5+O(x^6),x,6)

> 

lprint(sol); #solution is series

y(x) = series(1+1/2*x^2-1/6*x^3+1/24*x^4-1/120*x^5+O(x^6),x,6)

 

 

Download bug_report_dsolve_series_april_28_2025.mw

Controlling Variable Distribution in Polynomial Fo...

Asked by: salim-barzani 1550
polynomial expand pde
April 28 2025
2  5

In this work, I do not intend to expand all the variables across the monomials. Instead, I want to restrict the distribution to only the variables x,y,z,tx, y, z, tx,y,z,t, possibly raising them to appropriate powers as needed, until I obtain the desired solution and satisfy the conditions of my PDE tests. However, I am uncertain whether "monomial" is the correct term to use here.

S1.mw

trail-1.mw

why such different result from integrate when pull...

Asked by: nm 11353
integration int indefinite-integration
April 27 2025
2  3

These two expressions are the same, just pulled minus sign out

But look what happens when integrating them. the anti derivative of one is much more complicated than the other and contains complex numbers and logs. And no matter what I tried, I could not convert the complicated one to look same as the simpler result. Also could not verify the complicated one by back differentiating.

> 

integrand_1:=x^2*(-arctan(x) + x)*exp(-arctan(x) + x)/(x^2 + 1);

x^2*(-arctan(x)+x)*exp(-arctan(x)+x)/(x^2+1)

> 

integrand_2:=evala(integrand_1);

-x^2*(arctan(x)-x)*exp(-arctan(x)+x)/(x^2+1)

> 

simplify(integrand_1 - integrand_2)

0

> 

anti_1:=int(integrand_1,x);

(-arctan(x)+x)*exp(-arctan(x)+x)-exp(-arctan(x)+x)

> 

anti_2:=int(integrand_2,x);

-(1-x+((1/2)*I)*ln(1-I*x)-((1/2)*I)*ln(1+x*I))*(1-I*x)^(-(1/2)*I)*(1+x*I)^((1/2)*I)*exp(x)

> 

simplify(diff(anti_1,x)-integrand_1);

0

> 

simplify(diff(anti_2,x)-integrand_2);

Error, (in simpl/simpl/ReIm/sum) too many levels of recursion

> 

simplify(anti_1 - anti_2)

Error, (in simpl/simpl/ReIm/sum) too many levels of recursion

> 

simplify(anti_2);

(1/2)*(I*ln(1+x*I)-I*ln(1-I*x)+2*x-2)*(1-I*x)^(-(1/2)*I)*(1+x*I)^((1/2)*I)*exp(x)

> 

simplify(anti_2,ln);

(1/2)*(I*ln(1+x*I)-I*ln(1-I*x)+2*x-2)*(1-I*x)^(-(1/2)*I)*(1+x*I)^((1/2)*I)*exp(x)

 

 

Download int_strange_result_april_27_2025.mw

I would have expected same anti derivative to show.  To check, I used another software, and that one gave same anti-derivative for both integrands.

The questions I have: Why Maple gives such different result for same integrand? And how could one convert the one with the logs and complex numbers to the first one?

Maple 2025

First 9 10 11 12 13 14 15 Last Page 11 of 2421