## Issues with pdsolve...

will give me

which is indeed a solution of the PDE1

will give me

which is not a solution of the PDE2

However, both differential equations are equal, only the arguments are swapped around. Am I doing something wrong, or is this a bug?

Thanks

## Can't get an analytical solution, only numeric wit...

PDE := diff(u(x, t), t\$2) = (1/16)*(diff(u(x, t), x\$2))-(1/5)*(diff(u(x, t), t)); IBCs := u(x, 0) = x*(1-(1/2)*x), (D[2](u))(x, 0) = x*(1-(1/2)*x), u(0, t) = 0, (D[1](u))(1, t) = 0; Sol := pdsolve({IBCs, PDE}, HINT = f(x)*g(t)); Sol := subs(op([2, 2, 1], Sol) = n, Sol)

I thought that the addition of HINT wolud help but no.

The numeric solution gives the right answer but the analytical gives way too small numbers and wrong shape.

## How do I solve a partial differential equation wit...

Hi all,

I have a partial differential equation similar to the following:

Equation: f_x(x,y) + f_y(x,y) = f(x,y) + f(x,0),
Boundary value conditions: f(x,10) = f(10,y) = 0.

The solution is that f is identically equal to 0.

However, I am having trouble solving this equation in Maple. I type the following:

`pde := diff(f(x, y), x)+diff(f(x, y), y) = f(x, y)+f(x, 0);`

`bv1 := f(x, 10) = 0;`

`bv2 := f(10, y) = 0;`

`solution := pdsolve(pde, {bv1, bv2}, numeric, time = x, range = 0 .. 10);`

When Maple tries to evaluate the last expression, I get the error

Error, (in pdsolve/numeric/process_PDEs) PDEs can only contain dependent variables with direct dependence on the independent variables of the problem, got {f(x, 0)}

It seems to have difficulties with the expression "f(x,0)". Is there some trick to typing this in a way that makes Maple interpret it correctly?

Edit: I encounter the same problem, when I try to solve the ODE f'(x) = f(x) + f(0), where f(10) = 0.

Best regards.

## Wave Eqn in Polar Coordinates...

I am trying to solve the wave equation in polar coordinates.  The initial condition on u is given by f(r,theta) and the initial condition on u_t is zero.  The weight function is w(r).  I am not sure why it will not evaluate this as I know the solution remains finite on the domain (the unit disk).  Here is the code:

Wave Equation in Polar Coordinates

 >

Example:

 >
 (1)
 >
 (2)
 >
 >
 (3)
 >
 (4)
 >
 (5)
 >
 (6)
 >
 >

Any assistance would be greatly appreciated.

## How to collect specific expression?...

f2 := (diff(y(a, b), a)-(-(1/2)*x-1/2+(1/2)*sqrt(-3*x^2-2*x-3))/x^2)*(diff(y(a, b), b)-(-(1/2)*x-1/2-(1/2)*sqrt(-3*x^2-2*x-3))/x^2);
f := collect(expand(f2), [diff(y(a,b),a),diff(y(a,b),b),diff(y(a,b),a)*diff(y(a,b),b)]);