I wish to solve the Poisson Equation:$$u\_{xx}+u\_{yy}=1,$$with $u(x,y)$vanishing on $r=a$. 

I know that the final solution should be the sum of the homogenous part and the non-homogeneous part, which is $u(x,y)=u\_1+u\_2$, $u\_1$ is the solution of $$u\_{xx}+u\_{yy}=0, u=0 \ on\ r=a,$$ and $u\_2$ is the solution of $$u\_{xx}+u\_{yy}=1, u=0 \ on\ r=a. $$ I have no trouble to find $u\_1$, but how to solve $u\_2$? 

Any help, please.