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how can i solve pdes of the following form in maple

[tex] tc(t,x)\frac{\partial a(t,x)}{\partial t} - ta(t,x)\frac{\partial c(t,x)}{\partial t} = a(t,x)c(t,x) + t(a(t,x))^2 and be able to find both functions a(t,x) and b(t,x)

restart

u := proc (x, y) options operator, arrow; u[x](x)*(y/delta(x)-2*y^2/delta(x)^2+y^3/delta(x)^3+B*H*(1-3*y^2/delta(x)^2+2*y^3/delta(x)^3)/delta(x))/(3*B*H/delta(x)+2) end proc

int(u(x, y)^2, y = 0 .. delta(x))

I tried the following partial integration in MAPLE. But Maple says:

Error, (in u[x]) too many levels of recursion.

Analytically it is possible to evaluate the integral in the above lomits. Where lies the problem?

Dear my friends

Hi

I have a linear partial differential equation to solve.

> equ1:=F5*(diff(phi[2](r, theta), r, r)+(diff(phi[2](r, theta), r))/r+(diff(phi[2](r, theta), theta, theta))/r^2)+F3*phi[4](r,theta) = 0;

where F5 and F3 is constant and phi[2](r,theta) is unknown function.

I tried to solve this equation by the following Maple's command:

> pdsolve(equ1,phi[2](r,theta));

I'm having a few problems with differentiating in Maple. I have a potential function U given by:

U[c] := (1/2)*r^2+M[1]/r[1]+M[2]/r[2];

U[r] := r^2*(M[1]*M[2]-3)/(2*c^2)+((x(tau)+diff(y(tau), tau))^2+(y(tau)-(diff(x(tau), tau)))^2)^2/(8*c^2)+3*(M[1]/r[1]+M[2]/r[2])*((x(tau)+diff(y(tau), tau))^2+(y(tau)-(diff(x(tau), tau)))^2)/(2*c^2)-(M[1]/r[1]+M[2]/r[2])^2/(2*c^2)-M[1]*M[2]*(1/r[1]+(1/r[1]-1/r[2])*(1-3*mu-7*x(tau)-8*(diff(y(tau), tau)))+y(tau)^2*(M[2]/r[1]^3+M[1]/r[2]^3))/(2*c^2);

I have a nonlinear partial diff eq which I am sure has been categorized.  How do I go about finding literature on the eq & the approach to solve it.  I have visited various websites that have catalogs of nonlinear partial diff eq's.  The problem is notation is so NONSTANDARD I have no IDEA what I am reading.  I have included a PDF eq_of_choice.pdf with my notation which I am familiar with. ...

Included below is vector partial diff eq I am working with.  To get rid of the time deriv's I took the LaPlace transform & the remaining spatial eq in the s-domain is listed.  To make matters simpler I set beta = 0 to get rid of the curl of the field.  What remains is essentially the Helmholtz eq.  To simplify further I just found the homogeneous soln for the x direction only.

As can be seen the eigenfunctions are exponentials with s beneath...

I am working with a 3 dimensional vector partial diff eq that resembles the Helmholtz equation, but there is a curl of the vecotr field as the middle term.

ie-->LaPlacian(F)+2beta*gamma^2*curl(F)+gamma^2*F = 0

Anyone have knowledge or references for me to look over to solve this equation?

I would like to ask a 2-part question in Maple TA in which the correct response to the second part of the question is based on the student's response to the first part of the question.

Here is a simple example.

Question #1

A) What is 1+4 ?

B) What is 2 times your solution to part A?

Obviously, the correct answer to B is 10, but what if the student thought that the correct answer to A was 4? Then if they put 8 as the answer to B I would...

Recently, I submitted for publication to a peer-reviewed math journal

a formula for the n-th order implicit derivative given an implicit function G(z,w)=0.

i.e. dz/dw = - Gw/Gz where Gw and Gz are partial derivatives of G with respect to w and z, respectively. Anyway, I proved the general formula for d^n z/ dw^n.   I have since proved the generalization of this to implicit functions of several variables, G(z,w1,w2,...,w(N))=0. A good mathematician...

Hi,

When maples calculates Riemenn or Ricci tensor it displays the result in a notation which takes many lines or even pages. Can one replace derivatives with respect to x, y and z as fx, fy, fz instead of what is given by diff(f(x,y,z),x) etc.  and denote partial derivative with respect to t as just a dot. ( I know that maple can use dot to denote total derivative but I want it to denote partial derivative). and Can one write f(t,x,y,z) simply as f. These are...

How can Maple arrive at the following, for an unspecified function f(x,y), without knowing sufficient conditions (eg. whether the 2nd partials are continuous)?

> # From the ?diff help-page
> diff(f(x,y),x,y) - diff(f(x,y),y,x);
                                      0

Continuity of integrands isn't generally assumed by int (there's a separate optional parameter which enables it...