Question:How do I solve a partial differential equation with pdsolve, when the equation fixes a variable of the solution function?

Question:How do I solve a partial differential equation with pdsolve, when the equation fixes a variable of the solution function?

Maple

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.

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