What is the correct way to specify region where solution of a PDE is needed? For example, I am trying to verify my hand solution to this HW problem: Solve Poisson PDE in 2D
The above is the only information given in the textbook. So it is only in the upper half plane. If I type this
pde := VectorCalculus:-Laplacian(u(x,y),[x,y])=-1/(1+y);
pdsolve([pde,bc],u(x,y)) assuming y>0
But I get by hand using method of images is
So not exactly the same. I think I made mistake in my solution. But I am also not sure that just saying "assuming y>0" is doing what I think it is supposed to do. For example, suppose we want to solve the same PDE say in the first quadrant. Typing
pdsolve([pde,bc],u(x,y)) assuming y>0,x>0
Gives same solution. But the solution should be different. And typing
Gives same answer as well.
So I think I need another way to tell Maple the region of the solution. i.e. I need to tell Maple to use the Laplacian for the upper half plane only and not the Laplacian in the whole 2D space.
Any suggestions what to do and how to handle such problems?