I am currently working semi-infinite strip question that requires the use of separation of variables.
I inserted $q(x,y)=X(x)Y(y)$ into the Laplace equation provided in the image to then get $X''(x)Y(y) + X(x)Y''(y) = 0$. From here I get really confused as to how to move to forward. Do I do $X''(x)/X(x) + Y''(y)/Y(y) = 0$, then $X''(x)/X(x)=-k^2$ and $Y''(y)/(y)=k^2$? Can someone please help?
