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Hello all,

I have an ODE system (please see bellow) where my unknowns are S(t) and K(t), all the the other symbols are known parameters. This system, by given the initial values for S and K, that is, S(0)=100 and K(0)=20, I can solve numerically.

sys:= diff(S(t), t) = -eta*K(t)*S(t)/(w*N*(S(t)+K(t))), diff(K(t), t) = eta*K(t)*S(t)/(w*N*(S(t)+K(t)))+S(t)*(-z*eta*alpha*K(t)^2+(-z*eta*alpha*S(t)-(eta*alpha^2*S(t)^2-2*N*C[max]*w*eta*alpha*K(t)+((-N*w+z)*alpha+N*C[max]^2*w*eta)*w*N)*upsilon)*K(t)+N*S(t)*w*alpha*upsilon*(N*w-z))/((K(t)^2*alpha*z+3*K(t)*S(t)*alpha*z+(2*S(t)*z*alpha+upsilon)*S(t))*w*N)

In addition, I have an algebraic equation:

eq1:= -c2 + (K(t2)*S(t2)+w*N*S(t2))*z=0,

where S(t2) and K(t2) are the solutions of my ODE sys in S and K at t=t2. The t2 is unknown time variable. 

My question is: how can I find t2 such that my algebraic equation (eq1) is satisfied.

Thanks in advance,

Dmitry

 

 

hi.how i can dsolve couple linear equations with power series solutions or taylor series expantion?

file attached below.

thanks

 

TAYLOR.mw

A lot of my life is at the moment spent using solve to solve systems of equations, and then trying to weed through the solutions maple gives to find the ones I am interested in. Specifically i'd like to have a program that can weed through the solutions and eliminate those that include equalities of the  form p[i]=-p[j] or p[i]=0  where i and j are integers (or equalities of that form with the letter q replacing p). Specifically i don't want to exclude equalities of the form p[i]=-p[j]*something+something else-another thing.... as they can be useful (or equalities of that form with the letter q replacing p).

Here is a (simple) example of the kind of equations I am likely to be solving and their output from solve:
A := solve([p[1]*p[2]*p[3] = q[1]*q[2]*q[3], p[1]+p[3] = q[1]+q[3], p[2]^2+p[3]^2 = q[2]^2+q[3]^2])

I have some code which gets rid of solutions where one variable is set to 0 

with(ArrayTools);
GetRidOfDumbSolutions := proc (sols)
local Nsols, Npars, GoodSol, GoodSols, GoodSolsCounter, i, j;
Nsols := numelems(sols); Npars := numelems(sols[1]);
GoodSols := []; GoodSolsCounter := 0;
for i to Nsols do
GoodSol := 1;
for j to Npars do
if IsZero(rhs(sols[i, j]))
then GoodSol := 0
end if
end do;
if GoodSol = 1 then
GoodSols := Concatenate(1, GoodSols, sols[i])
end if
end do;
GoodSols
end proc

but i can't see how (in maple) to detect an expression of the form p[i]=-p[j] especiall if that is being written in 2-d math. (i don't quite understand the different maths environments or how to convert from one to another or to string)

Dear all;

 

Hello everybody, I need your help to dispaly some values obtained using my function f. When I run the code there is no results obtained. Many thanks.

restart:

# The vectors e(i) satify the folowing conditions
e(0)*e(1)=e(n-1) assuming  1<n;
e(0)*e(0)=e(2):
e(1)*e(1)=e(n-1) assuming  1<n: :
e(2)*e(1)=e(n) assuming  1<n:
#
for i from 1  to n-1 do
e(i)*e(0)=e(i+1);
end do:

# We define the function f
f:=e(0)->e(0)+(n-3)*e(1);
f:=e(1)->(n-2)*e(1);
for i from 2  to 3 do
f:=e(i)->(n+i-3)*e(i)+(i-1)*(n-3)*e(n-3+i);
end do:

for i from 4 to n do
f:=e(i)->(n+i-3)*e(i)
end do:

# We define the two vectors
x:=sum(alpha(k)*e(k),k=0..n);
y:=sum(beta(k)*e(k),k=0..n);

#Question : I would like to compute the following  but there is no display of the solution. 
(x*y);
f(x*y);
f(x);
f(y);
x*f(y);
f(x)*y;
f(x*y)- f(x)*y-x*f(y);

I have the following equation:

Diff(W(t), t) = -q*V*(sin(Phi)-sin(Psi[s]))/(2*h*Pi);

I solve it for rhs() = 0:

soln := solve([rhs((2)) = 0, Phi < 2*Pi], [Phi], allsolutions = true,explicit);

This works and I get this result:

Now I want to get the first zeros, which occur for _Z1 and _Z2 equal to 0. So I substitute:

subs(_Z2=0,(3));

and get

In other words, the substitution did not work.

The original problem is embedded in a larger sheet created with Maple 15 and there it does work. It fails on Maple 2015.2. I then pulled out the relevant pieces to make this example demonstrating the problem (see the attached sheet, which has some of my other (unsuccessful) attempts to diagnose what is going on). It seems like the created variables _Z1 and _Z2 are somehow not recognized at all.

The only way I can get the _Z2 terms out is to substitute 2=0. This is really too icky to seriously consider, though.

Anyone has seen this before?

FWIW: Maple 2015.2 on Mac OS X 10.10.5.

Thanks,

Mac Dude

Assumptions_test.mw

Dear all;

Thank you for helping me to solve this  question.

I solve an ode, but I have an error when I would like to plot the solution.

uanble to achieve continuous solution with requested accuracy of 0.1e-5 with maximum 128 point mesh (was able to get 0.14e-5), consider increasing `maxmesh` or using larger `abserr`
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

I try to increase the point mesh or take a large abserr but always I have the same problem.

 

restart:
with(plots):

ode := diff(y(x), x, x) = x*y(x)+sqrt(x);

ics := y(0) = 0, y(1) = 1;
sol:=dsolve({ode,ics}, numeric):
odeplot( sol,[x, y(x)], x=0..1, maxmesh=1000);

Dear friend! Hope every thing going fine with you. I need the solution of the following inqulity (for what values of a[1], a[2] and a[3] the equity hold) and it simplist form. 

 

3*a[1]*a[2]*a[3]-2*a[1]*a[2]-2*a[1]*a[3]-2*a[2]*a[3]+2*a[1]+2*a[2]+2*a[3]-1 <= 3*a[2]*a[1]*a[3]-((a[1]*a[2]*a[3]+1)/(a[2]*a[3]-a[3]+1)-1)*((a[1]*a[2]*a[3]+1)/(a[1]*a[3]-a[1]+1)-1)-((a[1]*a[2]*a[3]+1)/(a[2]*a[3]-a[3]+1)-1)*((a[1]*a[2]*a[3]+1)/(a[1]*a[2]-a[2]+1)-1)-((a[1]*a[2]*a[3]+1)/(a[1]*a[3]-a[1]+1)-1)*((a[1]*a[2]*a[3]+1)/(a[1]*a[2]-a[2]+1)-1)

 

I am waiting your quick response

Mob #: 0086-13001903838

Hi all,

 

I tried to find the real solution of the unlinear integral equation:

 

exp(-h^2/T)*(Int(exp(-x^2/T)*BesselI(0, h*x/T)*x, x = 0 .. 1))/T

 

but I got the warning and an complex solution:

 

 solve(subs(T = 1, eq)-.99 = 0, h)

Warning, solutions may have been lost

-1.232350242*10^(-32)-1.130417828*I

 

Can anyone help me to find a real solution for this issue (if possible)...?

I would like to thank you in advance.

 

EF.3.mwHi, I want to ask that how to find the exact solution of equation without applying any technique

Dear Collegues

I have a system of odes as follows

restart:
#gama1:=0.2:

#rhop:=5180:
#rhobf:=998.2:
#a[mu1]:=39.11:
#b[mu1]:=533.9:
#a[k1]:=7.47:
#b[k1]:=0:

Teq := N_bt*T(eta)^2*(exp(-(T(eta)-1)/(N_bt*(1+gama1)*(1+gama1*T(eta)))))^2*(diff(T(eta), eta, eta))*gama1^2*b[k1]+N_bt*T(eta)^2*exp(-(T(eta)-1)/(N_bt*(1+gama1)*(1+gama1*T(eta))))*(diff(T(eta), eta, eta))*gama1^2*a[k1]+2*N_bt*T(eta)*(exp(-(T(eta)-1)/(N_bt*(1+gama1)*(1+gama1*T(eta)))))^2*(diff(T(eta), eta, eta))*gama1*b[k1]+N_bt*T(eta)^2*(diff(T(eta), eta, eta))*gama1^2;


UEQ:=(a[mu1]*(-(diff(T(eta), eta))/(N_bt*(1+gama1)*(1+gama1*T(eta)))+(T(eta)-1)*gama1*(diff(T(eta), eta))/(N_bt*(1+gama1)*(1+gama1*T(eta))^2))*exp(-(T(eta)-1)/(N_bt*(1+gama1)*(1+gama1*T(eta))))+2*b[mu1]*(exp(-(T(eta)-1)/(N_bt*(1+gama1)*(1+gama1*T(eta)))))^2*(-(diff(T(eta), eta))/(N_bt*(1+gama1)*(1+gama1*T(eta)))+(T(eta)-1)*gama1*(diff(T(eta), eta))/(N_bt*(1+gama1)*(1+gama1*T(eta))^2)))*(diff(u(eta), eta))+(1+a[mu1]*exp(-(T(eta)-1)/(N_bt*(1+gama1)*(1+gama1*T(eta))))+b[mu1]*(exp(-(T(eta)-1)/(N_bt*(1+gama1)*(1+gama1*T(eta)))))^2)*(diff(u(eta), eta, eta))+1-exp(-(T(eta)-1)/(N_bt*(1+gama1)*(1+gama1*T(eta))))+exp(-(T(eta)-1)/(N_bt*(1+gama1)*(1+gama1*T(eta))))*rhop/rhobf;

I want to solve them with the following boundary conditions

T(0)=0, T(1)=1

u(0)=L*D(u)(0), D(u)(1)=0

However I tried, I cannot find the solution in a closed form. I want to know that is there a closed form solution for the above odes?

Thank you

Amir

Hi,

Im trying to study some questions and I'm using maple to verify my answers.

Theres a few polynomial factoring questions and linear equation questions Im trying to get

maple to show its solutions steps using showsolution() no matter where I put it  the function wont work.

Ive switched between math/text functions. Im still pretty new to maple but I can't find any information on how to do it

on the web/youtube.

 

Thanks in advance!

For the life of me I cannot find the method to do so.

 

So the solution would look like:

1. Euation

2 Step 2

3 Step 3

4 step 3+n

where n is the number of steps reuired.

Any help will be appreciated so very much.

.

.TIA

Larry C

 

 

I'm not sure why im getting a complex solution for evalf(h(-1/2)). Posted screenshot here:

http://prntscr.com/8abmta

The answer should be positive 6*2^(2/3) ≈ 9.52

 The computer returns

h(-1/2) =

=

The problem is that evalf((-1)^(1/3)) you get 0.500 + .866I

Is there no way to evaluate a second derivative of a real valued function which has a fractional exponent without receiving complex results? I don't have the time to look at each function and try to figure out what went wrong. I want to plug in any x value into a function defined for all reals and get a real result.

I tried  assume(x , 'real' ) , that did not do anything.

 

    

Dear all,

I am trying to solve the following partial differential equation (transport or advection equation) with given initial and boundary conditions:

restart: with(PDEtools):
sys := [v*diff(u(x,t), x) + diff(u(x,t), t) = 0, u(x,0) = exp(-x), u(0,t) = sin(t)];
pdsolve(sys);

But it does not work. The solution is (or should be): 

u(x, t) = exp(t*v-x)+Heaviside(t-x/v)*(sin(t-x/v)-exp(t*v-x))

I think the reason is that the interval for t (in [0, inf)) and x (in [0, 1]) is not specified. On the other hand, this works:

restart: with(PDEtools):
sys := [diff(u(x, t), t) = diff(u(x, t), x, x), u(0, t) = 0, u(1, t) = 0, u(x,0) = f(x)];
sol := pdsolve(sys);

How can I solve a PDE like the transport equation with given initial AND boundary conditions?

Thanks a lot

Cheers!

I'm having a problem with my student work, about to have a solution of 6 equations... Can help me in this file? i dont know how to solve this... this had-me a null solve...

 

 


Thanks for the help =)

restart

M1 := 0.15e5;

0.15e5

 

0.60e5

 

0

 

0.12e5

 

21000.00000

 

3

 

1

 

2.5

 

1

 

3

(1)

`&sigma;adm` := 175*10^6;

175000000

 

(1/300000)*L

 

210000000000

(2)

Atria := (3.5*12)/(LBC+LCD)

12.00000000

(3)

Ctria := LAB+LBC+(1/3)*(2*(LCD+LDE))

6.333333334

(4)

AiXil := Atria*Ctria

76.00000001

(5)

C := AiXil/Atria

6.333333334

(6)

``

``

``

SumFX := FAx;

FAx

(7)

SumFY := FAy+FCy+FEy-F5-QTria;

FAy+FCy+FEy-81000.00000

(8)

SumMA := FCy*(LAB+LBC)-F5*(LAB+LBC)+FEy*(LAB+LBC+LCD+LDE)+M1-MA-QTria*Ctria;

4*FCy-358000.0000+7.5*FEy-MA

(9)

NULL

``

``

EIYac := EIYo+`EI&theta;o`*x+M1*(x+0)^3/factorial(3);

EIYo+`EI&theta;o`*x+2500.000000*x^3

(10)

EIYce := EIYac+FCy*(x-4)^3/factorial(3)-F5*(x-4)^3/factorial(3)-q5*(x-4)^5/((3.5)*factorial(5));

EIYo+`EI&theta;o`*x+2500.000000*x^3+(1/6)*FCy*(x-4)^3-10000.00000*(x-4)^3-28.57142857*(x-4)^5

(11)

EIYef := EIYce+FEy*(x-7.5)^3/factorial(3)+(1/3)*q5*(x-7.5)^5/factorial(5);

EIYo+`EI&theta;o`*x+2500.000000*x^3+(1/6)*FCy*(x-4)^3-10000.00000*(x-4)^3-28.57142857*(x-4)^5+(1/6)*FEy*(x-7.5)^3+33.33333333*(x-7.5)^5

(12)

`EI&theta;ac` := diff(EIYac, x);

`EI&theta;o`+7500.000000*x^2

(13)

`EI&theta;ce` := diff(EIYce, x);

`EI&theta;o`+7500.000000*x^2+(1/2)*FCy*(x-4)^2-30000.00000*(x-4)^2-142.8571428*(x-4)^4

(14)

`EI&theta;ef` := diff(EIYef, x);

`EI&theta;o`+7500.000000*x^2+(1/2)*FCy*(x-4)^2-30000.00000*(x-4)^2-142.8571428*(x-4)^4+(1/2)*FEy*(x-7.5)^2+166.6666666*(x-7.5)^4

(15)

``

Mac := diff(`EI&theta;ac`, x);

15000.00000*x

(16)

Mce := diff(`EI&theta;ce`, x);

-45000.00000*x+FCy*(x-4)+240000.0000-571.4285712*(x-4)^3

(17)

Mef := diff(`EI&theta;ef`, x);

-45000.00000*x+FCy*(x-4)+240000.0000-571.4285712*(x-4)^3+FEy*(x-7.5)+666.6666664*(x-7.5)^3

(18)

``

Vac := diff(Mac, x);

15000.00000

(19)

Vce := diff(Mce, x);

-45000.00000+FCy-1714.285714*(x-4)^2

(20)

Vef := diff(Mef, x);

-45000.00000+FCy-1714.285714*(x-4)^2+FEy+1999.999999*(x-7.5)^2

(21)

``

x := 0:
``

`EI&theta;o` = 0

 

EIYo = 0

(22)

x := 4:

EIYo+4*`EI&theta;o`+160000.0000

(23)

x := 7.5:

EIYo+7.5*`EI&theta;o`+610931.2500+7.145833333*FCy

(24)

SOL := solve({CF1, CF2, CF3, CF4, SumFY, SumMA}, {EIyo, FAy, FCy, FEy, MA, `EIy&theta;o`});

"SOL:="

(25)

``

NULL

``

 

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