A thin rectangular homogeneous thermally conducting plate occupies the region $0 \leq x \leq a$, $0 \leq y \leq b$. The edge $y = 0$ is held at temperature $Tx(x − a)$, where T is a constant and the other edges are maintained at $0$. The other faces are insulated and there is no heat source or sink inside the plate. Find the steady state temperature inside the plate.
I was able to calculate the solution of laplace equation by seperation of variables but am stuck on the point at how to link these boundary conditions with the solution. Got C1(first constant) = 0 and value of k(which i assumed as the ratio constant for seperation of variables as k = n*pi/a. Stuck what to do next.
Sorry if I confuse you I am new to this.