## How to solve system of PDEs?...

I want to solve the following system of PDEs with Maple:

In fact, I want to determine q1,n1,p1,nn1,qn1,pn1 as a functions of pphi1 (assume  ne1(X,T)=(alpha/(2))*pphi1(X,T))

(mu, nu, beta, lambda, TE , alpha and TT are constant, but q1,n1,p1,nn1,qn1,pn1 depend on (X,T))

How do I do that?

> diff(q1(X, T), X)-lambda*(diff(n1(X, T), X)) = 0;

diff(pphi1(X, T), X)+TE*(diff(p1(X, T), X))-lambda*(diff(q1(X, T), X)) = 0;

-lambda*(diff(p1(X, T), X))+3*(diff(q1(X, T), X)) = 0;

-lambda*(diff(nn1(X, T), X))+diff(qn1(X, T), X) = 0;

-lambda*(diff(qn1(X, T), X))+beta*TT*(diff(pn1(X, T), X))-beta*(diff(pphi1(X, T), X)) = 0;

-lambda*(diff(pn1(X, T), X))+3*(diff(qn1(X, T), X)) = 0;

-mu*ne1(X, T)-nu*nn1(X, T)+n1(X, T) = 0;

## How to change coordinate?...

How can I transform the following differential equation from (x,t) to (X,T) coordinate, where, for example, X=x-alpha*t, T=beta*t (alpha and beta are constant)

diff(z, t)+(diff(R, x))*L+A*(diff(L, x))+diff(k, x, x)-(diff(k, t, t)) = 0

Thanks.

## How do I solve my Eqs. in Maple?...

Suppose two following Eqs.:

(1) du/dt+d(u*w)/dx=0

(2) dw/dt+wdw/dx=0

I want to expand u(x,t) and w(x,t) in the power series of epsilon

u=u0+epsilon*u1+epsilon^2*u2+…

w=w0+epsilon*w1+epsilon^2*w2+…

and change the variables x,t to X,T as follows

X=(x-alpha*t) and T=beta*t,

and solving Eqs. (1) and (2) for different order of epsilon (epsilon, epsilon^2, epsilon^3,…) to finding u0,w0,u1,w1,…

How do I do that?

Thanks.

## How do I extract all the coefficients of a partial...

d/dt(n_2)+d/dx (n0u2)

Thanks

## How to find equation of the intersection between ...

With the following command I can plot two spheres and plot them.

f1 := x^2+y^2+z^2 = 1

f2 := x+y+z = 1

with(plottools);

with(plots);

S1 := implicitplot3d(f1, x = -1 .. 1, y = -1 .. 1, z = -1 .. 1, style = patchnogrid, color = blue, scaling = constrained, axes = boxed)

S2 := implicitplot3d(f2, x = -1 .. 1, y = -1 .. 1, z = -1 .. 1, style = patchnogrid, color = gold, scaling = constrained, axes = boxed)

dispaly(S1,S2)

My questions are:

1- How can I display (highlight) the circle which is the intersection between these two sphere on the same figure?

2- How can I find the equation of this circle?

Thank you.

## printing ifactor output in order and from left...

ifactor(8650368) produces

2503  *  2^7 * 3^3

how can I produce the output with factors in order from small to large and printed f rom left

2^7 * 3^3 * 2503

## Solving function to vo/vs ...

Hi

I have 3 equations

eq1 := vs = (Rs+Z)*i1+Z*i3

eq2 := A*vi = Z*i1+(Z+Rf+ro)*i3

eq3:= vo = (Rf+Z)*i3+Z*i1

and I want to solve for vo/vs . How to do that ?

the expected solution is

## difficult integration from zero to infinity...

restart; with(LinearAlgebra); int(exp(-(ln(z/(snr*B^2))+4*sigma^2)^2/(32*sigma^2))*eta^2*(y/z)^((1/2)*eta^2-1)/(z*sqrt(32*Pi*sigma^2)*(2*sqrt(y*z))*(2*A[o]^(eta^2))), z, z = y/A[o]^2 .. infinity);

restart; with(LinearAlgebra); int(exp(-(ln(z/(snr*B^2))+4*sigma^2)^2/(32*sigma^2))*eta^2*(y/z)^((1/2)*eta^2-1)/(z*sqrt(32*Pi*sigma^2)*(2*sqrt(y*z))*(2*A[o]^(eta^2))), z, z = y/A[o]^2 .. infinity)

## PDSolve in Maple 11...

I'm trying to execute the program, which can be found here http://www.maplesoft.com/support/help/Maple/view.aspx?path=examples/pdsolve_boundaryconditions , but it does not work. I copied exactly what is written there:

restart; with(PDEtools):
U := diff_table(u(x,t)):
pde[1] := U[t]+c*U[x]=-lambda*U[];
bc[1] := eval(U[], t=0) = phi(x);
sys[1] := [pde[1], bc[1]];
pdsolve(sys[1]);

But after last command it just sais that

Error, (in pdsolve/sys/info) found functions with same name but depending on different arguments in the given DE system: [u(x,t), u(x,0)]

What's wrong?

## problem with calculation in Maple v11 and v18...

Dear Community Members,

We have problem with calculation in Maple v11 and v18. when we make a calculation by using maple v11 and v18, we was not able to get the solution as you see enclosed. when we clicked to "enter + ; ", programme does not run.

## using an error in loop...

Hello

I have a loop with the do structure but there is an error in the loop .

how can I continue the loop by error or disregard it?

## Solving an ode : Warning, it is required that the...

Hello,

could you help me solve this error ? I don't understand what it means.

> eq3:=diff(x(t),t,t)+Gamma*diff(x(t),t)+omega[0]^2*(x(t)-(diff(x(t),t,t)+Gamma*diff(x(t),t)+omega[0]^2*x(t)+omega[0]^2*X[0])/omega[0]^2) = -omega[0]^2*X[0]:
> dsolve(eq3);
Warning, it is required that the numerator of the given ODE depends on the highest derivative. Returning NULL.

Thanks.

## Integral problem with maple...

I have a great problem with this integral and Maple gives two answers completely different:

so I get two different results :

or this:

In the first integral A get Lommels2 and If I get the Integral by using Taylor of  and after that I resum I get Lommels1.

Thank you.

## How to get the roots?...

Greetings everyone. I tried to get the roots of this polynomial by using allvalues command. But I got the roots in indeces instead of the value of the roots.

what should i do?

## Error, too many levels of recursion...

Hello! I wrote a program in Maple but it doesn't work. It crashes with the following error: "Error, (in r_nach_1[3]) too many levels of recursion". I am a newbie in Maple and don't know how to solve this problem. A part of my program that causes the error is given below. Many thanks!

maple.mws

restart;
t1F := 20: A11 := 2.5*10^(-3): c1 := 4*10^2: ss1 := 0.5*10^(-2):
pI1 := 0.4*10^(-1): r1max := 0.6*10^(-2): procent:=0.2:
A12 := procent*A11: B1:=-1: alpha:=0.000001:

beta1:=0.5: r_nach_1[1]:=0: r_nach_1[2]:=0.2*10^(-2):

iter_psi_c1_1:=proc(t) 0 end proc: iter_psi_c2_1:=proc(t) 0 end proc:
s1[1]:=proc(t) 0 end proc:

for i from 1 to 2 do

_p11 := evalf(dsolve({
diff(p1(t), t) = A11*(p1(t)-'s1'[i](t))+B1*(r_nach_1[i+1](t)-r_nach_1[i](t))+A12*(p1(t)-'s1'[i](t))^2+ss1,
p1(0) = pI1}, numeric,method = dverk78, abserr = 1.*10^(-8), relerr = 1.*10^(-8),optimize,output = listprocedure, known=[s1[i],iter_psi_c1_1,iter_psi_c2_1])):

p1F := rhs(_p11(t1F)[2]):
s1[i+1] := subs(_p11, p1(t)):

q11 := evalf(dsolve({diff(q1(t), t) = c1*r_nach_1[i+1](t), q1(0) = 0},numeric,range=0..t1F,known=[iter_psi_c1_1,iter_psi_c2_1])):

q1F := rhs(q11(t1F)[2]):

F[i]:= beta1*q1F;

_psi_c1_1 :=
evalf(dsolve({
diff(psi_c1_1(t), t) = A11+2*A12*('s1'[i+1](t)-'s1'[i](t))*psi_c1_1(t), psi_c1_1(t1F) =  -1+beta1},numeric,method = dverk78, abserr = 1.*10^(-8), relerr = 1.*10^(-8),optimize,known=[s1[i],s1[i+1]],output=listprocedure)):

_psi_c2_1 :=evalf(dsolve({
diff(psi_c2_1(t), t) = 0, psi_c2_1(t1F) =  -beta1},numeric,output=listprocedure)):
iter_psi_c1_1 := op([2,2],_psi_c1_1):
iter_psi_c2_1 := op([2,2],_psi_c2_1):

r_nach_1[i+2] := t-> r_nach_1[i+1](t) +  alpha*(B1*(iter_psi_c1_1(t)) + (c1*iter_psi_c2_1(t))):

_p11 := evalf(dsolve({
diff(p1(t), t) = A11*(p1(t)-'s1'[i+1](t))+B1*(r_nach_1[i+2](t)-r_nach_1[i+1](t))+A12*(p1(t)-'s1'[i+1](t))^2+ss1,
p1(0) = pI1}, numeric,method = dverk78, abserr = 1.*10^(-8), relerr = 1.*10^(-8),optimize, output = listprocedure, known=[s1[i+1],iter_psi_c1_1,iter_psi_c2_1])):

p1F := rhs(_p11(t1F)[2]):

s1[i+2] := subs(_p11, p1(t)):

q11 := evalf(dsolve({diff(q1(t), t) = c1*r_nach_1[i+2](t), q1(0) = 0},numeric,range=0..t1F,known=[iter_psi_c1_1,iter_psi_c2_1])):

q1F := rhs(q11(t1F)[2]):

F[i+1]:= beta1*q1F;

od:
Error, (in r_nach_1[3]) too many levels of recursion

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