Maple Questions and Posts

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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+`Λ__p`

-S*µ__C+Lambda__p

(6)

NULL

``

(7)

E3 := -S__A*µ__A+`Λ__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 := `Λ__p`-(`ϕ`*`θ__B`*I__A/N__p+µ__C)*S+`ω__B`*I__B

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

(17)

E2 := `ϕ`*`θ__B`*I__A*S/N__p-`ω__B`*I__B-(`σ__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 := `Λ__A`-(µ__A+`ϕ`*`α__B`*I__B/N__p)*S__A+`δ__A`*I__A

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

(20)

E4 := `ϕ`*`α__B`*I__B*S__A/N__p-(µ__A+`δ__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) = -`ϕ`*`θ__B`*I__A/N__p-µ__C, (1, 2) = `ω__B`, (1, 3) = 0, (1, 4) = -`ϕ`*`θ__B`*S/N__p, (2, 1) = `ϕ`*`θ__B`*I__A/N__p, (2, 2) = -`ω__B`-`σ__B`-µ__C, (2, 3) = 0, (2, 4) = `ϕ`*`θ__B`*S/N__p, (3, 1) = 0, (3, 2) = -`ϕ`*`α__B`*S__A/N__p, (3, 3) = -µ__A-`ϕ`*`α__B`*I__B/N__p, (3, 4) = `δ__A`, (4, 1) = 0, (4, 2) = `ϕ`*`α__B`*S__A/N__p, (4, 3) = `ϕ`*`α__B`*I__B/N__p, (4, 4) = -µ__A-`δ__A`})

Matrix(%id = 18446746579340105118)

(26)

S := `Λ__p`/µ__C

Lambda__p/µ__C

(27)

S__A := `Λ__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) = -`ϕ`*`θ__B`*I__A/N__p-µ__C, (1, 2) = `ω__B`, (1, 3) = 0, (1, 4) = -`ϕ`*`θ__B`*S/N__p, (2, 1) = `ϕ`*`θ__B`*I__A/N__p, (2, 2) = -`ω__B`-`σ__B`-µ__C, (2, 3) = 0, (2, 4) = `ϕ`*`θ__B`*S/N__p, (3, 1) = 0, (3, 2) = -`ϕ`*`α__B`*S__A/N__p, (3, 3) = -µ__A-`ϕ`*`α__B`*I__B/N__p, (3, 4) = `δ__A`, (4, 1) = 0, (4, 2) = `ϕ`*`α__B`*S__A/N__p, (4, 3) = `ϕ`*`α__B`*I__B/N__p, (4, 4) = -µ__A-`δ__A`})

Matrix(%id = 18446746579340107518)

(32)

J := Matrix(4, 4, {(1, 1) = -µ__C, (1, 2) = `ω__B`, (1, 3) = 0, (1, 4) = -`β__1`, (2, 1) = 0, (2, 2) = -`ω__B`-`σ__B`-µ__C, (2, 3) = 0, (2, 4) = -`β__1`, (3, 1) = 0, (3, 2) = -`β__2`, (3, 3) = -µ__A, (3, 4) = `δ__A`, (4, 1) = 0, (4, 2) = `β__2`, (4, 3) = 0, (4, 4) = -µ__A-`δ__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) = `ρ__A`, (3, 6) = `ρ__F`, (3, 7) = -(-1+k)*`ρ__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) = -`ρ__A`-q__A-µ, (5, 6) = 0, (5, 7) = k*`ρ__Q`, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = -delta*(-1+a), (6, 5) = 0, (6, 6) = -`ρ__F`-q__F-`δ__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) = -`ρ__Q`-`δ__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

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

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

Dear all 
I have a double integral, i want to compute this integral and verify if the pproposed solution verify the proposed equation or not. 
I can modify the right hand side of my equation or the exact solution, so that my equation has an exact solution with simple form of right hand side. 

exact_solution.mw

Thank you for your help 

FYI;

 

You might have to try the command more than one time to see the above crash. Here is the worksheet

restart;

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 13 and is the same as the version installed in this computer, created April 22, 2025, 15:14 hours Eastern Time.`

restart;

ode:=x^2-2*x*y(x)+5*y(x)^2 = (x^2+2*x*y(x)+y(x)^2)*diff(y(x),x);

x^2-2*x*y(x)+5*y(x)^2 = (x^2+2*x*y(x)+y(x)^2)*(diff(y(x), x))

sol:=y(x) = (-1/2*exp(RootOf(-exp(_Z)^2*ln(x*(exp(_Z)-2))+2*_C7*exp(_Z)^2+_Z*exp(_Z)^2+4*exp(_Z)*ln(x*(exp(_Z)-2))-8*_C7*exp(_Z)-4*exp(_Z)*_Z-2*exp(_Z)-4*ln(x*(exp(_Z)-2))+8*_C7+4*_Z+6))^2+3*exp(RootOf(-exp(_Z)^2*ln(x*(exp(_Z)-2))+2*_C7*exp(_Z)^2+_Z*exp(_Z)^2+4*exp(_Z)*ln(x*(exp(_Z)-2))-8*_C7*exp(_Z)-4*exp(_Z)*_Z-2*exp(_Z)-4*ln(x*(exp(_Z)-2))+8*_C7+4*_Z+6))-6+2*(exp(RootOf(-exp(_Z)^2*ln(x*(exp(_Z)-2))+2*_C7*exp(_Z)^2+_Z*exp(_Z)^2+4*exp(_Z)*ln(x*(exp(_Z)-2))-8*_C7*exp(_Z)-4*exp(_Z)*_Z-2*exp(_Z)-4*ln(x*(exp(_Z)-2))+8*_C7+4*_Z+6))^2-6*exp(RootOf(-exp(_Z)^2*ln(x*(exp(_Z)-2))+2*_C7*exp(_Z)^2+_Z*exp(_Z)^2+4*exp(_Z)*ln(x*(exp(_Z)-2))-8*_C7*exp(_Z)-4*exp(_Z)*_Z-2*exp(_Z)-4*ln(x*(exp(_Z)-2))+8*_C7+4*_Z+6))+9)^(1/2))/(1/2*exp(RootOf(-exp(_Z)^2*ln(x*(exp(_Z)-2))+2*_C7*exp(_Z)^2+_Z*exp(_Z)^2+4*exp(_Z)*ln(x*(exp(_Z)-2))-8*_C7*exp(_Z)-4*exp(_Z)*_Z-2*exp(_Z)-4*ln(x*(exp(_Z)-2))+8*_C7+4*_Z+6))^2-3*exp(RootOf(-exp(_Z)^2*ln(x*(exp(_Z)-2))+2*_C7*exp(_Z)^2+_Z*exp(_Z)^2+4*exp(_Z)*ln(x*(exp(_Z)-2))-8*_C7*exp(_Z)-4*exp(_Z)*_Z-2*exp(_Z)-4*ln(x*(exp(_Z)-2))+8*_C7+4*_Z+6)))*x:

odetest(sol,ode);

 

Download crash_maple_2025_april_27_2025.mw

Hopefully a fix could be found for this.

MapleCloud opend from Maple2025 and 2024.

Has this extended scrollbar always been like this?
Maybe it is a browser thing.
Which browser is Maple using?
Are there any settings I could adjust?

When using FunctionAdvisor(branch_cuts, f(x), plot="2D"); how do I enforce discontinuous lines be presented with option discont=true?

How i can get this special parameter i try to do substitution in another mw file but stilli can't reach this parameter and without this parameter my PDE is not give me zero so i have to find this r[i] parameter, some letter of my mw file are not similar to paper but r[i]=l[i] as mention is paper al clear and i found all structure just this remain, i am looking for equation (14), thanks for any help 

restart

with(PDEtools)

with(LinearAlgebra)

NULL

with(SolveTools)

_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.

 

NULL

declare(u(x, y, z, t))

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

(1)

declare(f(x, y, z, t))

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

(2)

pde1 := a*(diff(u(x, y, z, t), x, t))-((a^4-6*a^2*b^2+b^4)*(1/16))*(diff(u(x, y, z, t), `$`(x, 4)))-(1/4)*(3*(-a^2+b^2))*(diff(u(x, y, z, t)^2, `$`(x, 2)))+alpha*(diff(u(x, y, z, t), `$`(x, 2)))+beta*(diff(u(x, y, z, t), x, y))+delta*(diff(u(x, y, z, t), x, z))+lambda*(diff(u(x, y, z, t), `$`(z, 2)))+mu*(diff(u(x, y, z, t), y, z))+mu^2*(diff(u(x, y, z, t), `$`(y, 2)))/(4*lambda)

a*(diff(diff(u(x, y, z, t), t), x))-(1/16)*(a^4-6*a^2*b^2+b^4)*(diff(diff(diff(diff(u(x, y, z, t), x), x), x), x))-(3/4)*(-a^2+b^2)*(2*(diff(u(x, y, z, t), x))^2+2*u(x, y, z, t)*(diff(diff(u(x, y, z, t), x), x)))+alpha*(diff(diff(u(x, y, z, t), x), x))+beta*(diff(diff(u(x, y, z, t), x), y))+delta*(diff(diff(u(x, y, z, t), x), z))+lambda*(diff(diff(u(x, y, z, t), z), z))+mu*(diff(diff(u(x, y, z, t), y), z))+(1/4)*mu^2*(diff(diff(u(x, y, z, t), y), y))/lambda

(3)

Tr := {beta = alpha, delta = alpha, mu = 2*lambda}

{beta = alpha, delta = alpha, mu = 2*lambda}

(4)

pde := subs(Tr, pde1)

a*(diff(diff(u(x, y, z, t), t), x))-(1/16)*(a^4-6*a^2*b^2+b^4)*(diff(diff(diff(diff(u(x, y, z, t), x), x), x), x))-(3/4)*(-a^2+b^2)*(2*(diff(u(x, y, z, t), x))^2+2*u(x, y, z, t)*(diff(diff(u(x, y, z, t), x), x)))+alpha*(diff(diff(u(x, y, z, t), x), x))+alpha*(diff(diff(u(x, y, z, t), x), y))+alpha*(diff(diff(u(x, y, z, t), x), z))+lambda*(diff(diff(u(x, y, z, t), z), z))+2*lambda*(diff(diff(u(x, y, z, t), y), z))+lambda*(diff(diff(u(x, y, z, t), y), y))

(5)

pde_linear, pde_nonlinear := selectremove(proc (term) options operator, arrow; not has((eval(term, u(x, y, z, t) = T*u(x, y, z, t)))/T, T) end proc, expand(pde))

a*(diff(diff(u(x, y, z, t), t), x))-(1/16)*(diff(diff(diff(diff(u(x, y, z, t), x), x), x), x))*a^4+(3/8)*(diff(diff(diff(diff(u(x, y, z, t), x), x), x), x))*a^2*b^2-(1/16)*(diff(diff(diff(diff(u(x, y, z, t), x), x), x), x))*b^4+alpha*(diff(diff(u(x, y, z, t), x), x))+alpha*(diff(diff(u(x, y, z, t), x), y))+alpha*(diff(diff(u(x, y, z, t), x), z))+lambda*(diff(diff(u(x, y, z, t), z), z))+2*lambda*(diff(diff(u(x, y, z, t), y), z))+lambda*(diff(diff(u(x, y, z, t), y), y)), (3/2)*(diff(u(x, y, z, t), x))^2*a^2-(3/2)*(diff(u(x, y, z, t), x))^2*b^2+(3/2)*u(x, y, z, t)*(diff(diff(u(x, y, z, t), x), x))*a^2-(3/2)*u(x, y, z, t)*(diff(diff(u(x, y, z, t), x), x))*b^2

(6)

NULL

eq17 := u(x, y, z, t) = (-a^4+6*a^2*b^2-b^4)*((diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)-(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^2)/(2*a^2-2*b^2)

``NULL

betai := k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i]

k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i]

(7)

W := w[i] = ((a^4-6*a^2*b^2+b^4)*k[i]^2-16*lambda*l[i]^2+(-32*lambda*r[i]-16*alpha)*l[i]-16*lambda*r[i]^2-16*alpha*r[i]-16*alpha)/(16*a)

AA := A[12] = (16*(l[1]-l[2]+r[1]-r[2])^2*lambda+3*(k[1]-k[2])^2*(a^2+2*a*b-b^2)*(a^2-2*a*b-b^2))/(16*(l[1]-l[2]+r[1]-r[2])^2*lambda+3*(k[1]+k[2])^2*(a^2+2*a*b-b^2)*(a^2-2*a*b-b^2))

F2 := 1+exp(beta[1])+A[1, 2]*exp(beta[1]+beta[2])+exp(beta[2])

1+exp(beta[1])+A[1, 2]*exp(beta[1]+beta[2])+exp(beta[2])

(8)

NULL

F22 := f(x, y, z, t) = 1+exp((a^4*t*k[1]^3-6*a^2*b^2*t*k[1]^3+b^4*t*k[1]^3-16*lambda*t*k[1]*l[1]^2-32*lambda*t*k[1]*l[1]*r[1]-16*lambda*t*k[1]*r[1]^2+16*a*y*k[1]*l[1]+16*a*z*k[1]*r[1]-16*alpha*t*k[1]*l[1]-16*alpha*t*k[1]*r[1]+16*a*x*k[1]-16*alpha*t*k[1]+16*a*eta[1])/(16*a))+exp((a^4*t*k[2]^3-6*a^2*b^2*t*k[2]^3+b^4*t*k[2]^3-16*lambda*t*k[2]*l[2]^2-32*lambda*t*k[2]*l[2]*r[2]-16*lambda*t*k[2]*r[2]^2+16*a*y*k[2]*l[2]+16*a*z*k[2]*r[2]-16*alpha*t*k[2]*l[2]-16*alpha*t*k[2]*r[2]+16*a*x*k[2]-16*alpha*t*k[2]+16*a*eta[2])/(16*a))

eq := eval(eq17, F22)

u(x, y, z, t) = (-a^4+6*a^2*b^2-b^4)*((k[1]^2*exp((1/16)*(a^4*t*k[1]^3-6*a^2*b^2*t*k[1]^3+b^4*t*k[1]^3-16*lambda*t*k[1]*l[1]^2-32*lambda*t*k[1]*l[1]*r[1]-16*lambda*t*k[1]*r[1]^2+16*a*y*k[1]*l[1]+16*a*z*k[1]*r[1]-16*alpha*t*k[1]*l[1]-16*alpha*t*k[1]*r[1]+16*a*x*k[1]-16*alpha*t*k[1]+16*a*eta[1])/a)+k[2]^2*exp((1/16)*(a^4*t*k[2]^3-6*a^2*b^2*t*k[2]^3+b^4*t*k[2]^3-16*lambda*t*k[2]*l[2]^2-32*lambda*t*k[2]*l[2]*r[2]-16*lambda*t*k[2]*r[2]^2+16*a*y*k[2]*l[2]+16*a*z*k[2]*r[2]-16*alpha*t*k[2]*l[2]-16*alpha*t*k[2]*r[2]+16*a*x*k[2]-16*alpha*t*k[2]+16*a*eta[2])/a))/(1+exp((1/16)*(a^4*t*k[1]^3-6*a^2*b^2*t*k[1]^3+b^4*t*k[1]^3-16*lambda*t*k[1]*l[1]^2-32*lambda*t*k[1]*l[1]*r[1]-16*lambda*t*k[1]*r[1]^2+16*a*y*k[1]*l[1]+16*a*z*k[1]*r[1]-16*alpha*t*k[1]*l[1]-16*alpha*t*k[1]*r[1]+16*a*x*k[1]-16*alpha*t*k[1]+16*a*eta[1])/a)+exp((1/16)*(a^4*t*k[2]^3-6*a^2*b^2*t*k[2]^3+b^4*t*k[2]^3-16*lambda*t*k[2]*l[2]^2-32*lambda*t*k[2]*l[2]*r[2]-16*lambda*t*k[2]*r[2]^2+16*a*y*k[2]*l[2]+16*a*z*k[2]*r[2]-16*alpha*t*k[2]*l[2]-16*alpha*t*k[2]*r[2]+16*a*x*k[2]-16*alpha*t*k[2]+16*a*eta[2])/a))-(k[1]*exp((1/16)*(a^4*t*k[1]^3-6*a^2*b^2*t*k[1]^3+b^4*t*k[1]^3-16*lambda*t*k[1]*l[1]^2-32*lambda*t*k[1]*l[1]*r[1]-16*lambda*t*k[1]*r[1]^2+16*a*y*k[1]*l[1]+16*a*z*k[1]*r[1]-16*alpha*t*k[1]*l[1]-16*alpha*t*k[1]*r[1]+16*a*x*k[1]-16*alpha*t*k[1]+16*a*eta[1])/a)+k[2]*exp((1/16)*(a^4*t*k[2]^3-6*a^2*b^2*t*k[2]^3+b^4*t*k[2]^3-16*lambda*t*k[2]*l[2]^2-32*lambda*t*k[2]*l[2]*r[2]-16*lambda*t*k[2]*r[2]^2+16*a*y*k[2]*l[2]+16*a*z*k[2]*r[2]-16*alpha*t*k[2]*l[2]-16*alpha*t*k[2]*r[2]+16*a*x*k[2]-16*alpha*t*k[2]+16*a*eta[2])/a))^2/(1+exp((1/16)*(a^4*t*k[1]^3-6*a^2*b^2*t*k[1]^3+b^4*t*k[1]^3-16*lambda*t*k[1]*l[1]^2-32*lambda*t*k[1]*l[1]*r[1]-16*lambda*t*k[1]*r[1]^2+16*a*y*k[1]*l[1]+16*a*z*k[1]*r[1]-16*alpha*t*k[1]*l[1]-16*alpha*t*k[1]*r[1]+16*a*x*k[1]-16*alpha*t*k[1]+16*a*eta[1])/a)+exp((1/16)*(a^4*t*k[2]^3-6*a^2*b^2*t*k[2]^3+b^4*t*k[2]^3-16*lambda*t*k[2]*l[2]^2-32*lambda*t*k[2]*l[2]*r[2]-16*lambda*t*k[2]*r[2]^2+16*a*y*k[2]*l[2]+16*a*z*k[2]*r[2]-16*alpha*t*k[2]*l[2]-16*alpha*t*k[2]*r[2]+16*a*x*k[2]-16*alpha*t*k[2]+16*a*eta[2])/a))^2)/(2*a^2-2*b^2)

(9)

pdetest(eq, pde)

Download fusion-undon.mw

Encountered this error using patmatch with condition. I have changed my code since then  to avoid such cases.

But do you think this is valid error? It only happens when adding conditional. 

interface(version);

restart;

RHS:=1/2/lambda(y)*f(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*a+1/2/lambda(y)*f(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*b-1/lambda(y)*f(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*y-1/2/lambda(y)^2*D(f)(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*a*b+1/2/lambda(y)^2*D(f)(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*a*y+1/2/lambda(y)^2*D(f)(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*b*y-1/2/lambda(y)^2*D(f)(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*y^2;

(1/2)*f(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*a/lambda(y)+(1/2)*f(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*b/lambda(y)-f(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*y/lambda(y)-(1/2)*(D(f))(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*a*b/lambda(y)^2+(1/2)*(D(f))(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*a*y/lambda(y)^2+(1/2)*(D(f))(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*b*y/lambda(y)^2-(1/2)*(D(f))(RootOf(f(_Z)*a*b-f(_Z)*a*y-f(_Z)*b*y+f(_Z)*y^2+lambda(y)^2))*y^2/lambda(y)^2

patmatch(RHS,F::anything*lambda(y)^(n::anything)+H::anything,'la')

true

patmatch(RHS,conditional(F::anything*lambda(y)^(n::anything)+H::anything, not (_has(H,lambda(y)) or _has(n,y))),'la')

Error, (in PatternMatching:-AlgStruct:-Match) string or symbol expected for substring

 

 

Download error_patmatch_april_18_2025.mw

I have a problem calculating integral analytically.

Can anyone help me in this regard?

Thanks

problem_2_integral_&_moshtagh.mw

Occasionally I want to convert 2D-Math input to 1D-Math input. This is either not fully working with comments or changes the format. Example:

Try converting the input below to Maple 1D-Math (select -> right click -> 2D-Math -> convert to -> 1D-Math)

statement

statement

(1)

The*comment*dissapears:

statement;

 

statement

(2)

The Maple Input at the top can be converted by selecting the style C Maple Input from the edit tab but the font changes not to the default font for 1D Math-Input;

statement

statement

(3)

The above is in italic and not in bold. However the default for 1D-Math Input is the following

statement

statement

(4)

 

NULL

Also pasting code with comments in MaplePrimes (function insert code snippet) removes comments.

Any other ways? Ideally, I would also like to convert a whole document in one go, That is probably asked too much.

Download convert_comment_to_1D.mw

in try to figure out why in some function i can find this critical point for ploting i need that point , untill now i just find in one function and other i can't and my program not runing for other and really this is make problem for my invistigation i want to fixed that and i upload that file i did and that file i can't find it for , thanks for any help?

line-undone.mw

Line-1-Done.mw

I can't find the help page for Abel second kind, class B. 

Maple has help page for Abel second kind, class A and Abel second kind, class C. But not for class B. 

Here is an example of Abel second kind class B

ode:=(3*t*y(t)+y(t)^2)+(t^2+t*y(t))*diff(y(t),t)=0;
DEtools:-odeadvisor(ode)

I wanted to know the difference and the transformation used for class B to make it Abel first kind.

I googled and can't find it. Also local help skips over class B.

Is this documented somewhere else?

btw, find error on the help page for class A. Transformation used is wrong. Will leave this for another question.

I'm not currently working on the topic of fluids and I'm not very familiar with it. However, my partner is working on it and is using other software. They have a question about whether Maple can handle this kind of work. Are there any examples available? I’d appreciate any help

thanks!

Dear Maple experts,

is there a possibility/command to get a vizualization of the output of the command FeedbackConnect?

I was thinking of something like this:


as it is given on the maple-help page for that command (but not generated via a maple command as far as I understood)

Thanks in advance !

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