# Question:pdsolve and laplace PDE on semi-infinite domain

## Question:pdsolve and laplace PDE on semi-infinite domain

Maple 2019

Hello Maple experts;

I am not able to understand why Maple 2019 can solve Laplace PDE in 2D Catersian on semi-infinite domain, when the infinity is along the Y direction, but not along the X direction, since the solution method is exactly the same.

Here is the code

restart;

#right one, Maple can not solve
pde := diff(u(x, y), x\$2)+diff(u(x, y), y\$2) = 0:
bc_left_edge := u(0, y) = 0:
bc_bottom_edge:= u(x, 0) = 0:
bc_top_edge:= u(x, 1) = A:
bc:=bc_left_edge ,bc_top_edge,bc_bottom_edge:
sol:=pdsolve([pde, bc],HINT = boundedseries(x = infinity)) assuming x>0,y>0;

#left one, Maple can solve
pde := diff(u(x, y), x\$2)+diff(u(x, y), y\$2) = 0:
bc_left_edge := u(0, y) = 0:
bc_bottom_edge:= u(x, 0) = 0:
bc_right_edge:= u(1, y) = A:
bc:=bc_left_edge ,bc_right_edge,bc_bottom_edge:
sol:=pdsolve([pde, bc],HINT = boundedseries(y = infinity)) assuming x>0,y>0;

Here is screen shot.

Maple can solve both cases if I remove the HINT. But the solution it gives is not as simple as using the HINT and contains unknown constants (_C5) that is why I use the HINT.

But the main question is, since both problems are exactly the same, why Maple can solve one and not the other when using the HINT? Is there something I am doing wrong?

Maple 2019 on windows 10 and Physics cloud version 333.

Thank you

﻿