# Partial Differential Equations: Dirichlet problem for the Laplace equation on half-space with boundary condition

Consider the Dirichlet problem for the Laplace equation on half-space with the boundary condition $$f(x)=\chi _{[0,\infty)}(x)$$. Use the exact solution and find a functon $$g:\mathbb{R}\rightarrow \mathbb{R}$$ such that $$u(x,y)=g(x/y)$$

Really need help with this question!!Please! Any help would be highly appreciated!