Translate the following into a PDE with boundary conditions.

A thin, homogeneous, rectangular plate coincides with the region defined by $0\leq x\leq a,0\leq y\leq b$. The left end and the bottom plate of the plate are insulated. The top of the plate is held at temperature zero, and the right end of the plate is held at temperature $\sin\!\left(\frac{\pi y}{b}\right)$. The temperature is at a steady state everywhere on the plate. How to enter the answers.

The PDE is
When $t\geq 0$ the boundary values / initial conditions are:
Left end is insulated
Bottom is insulated:
Top held at temperature zero:
Right end held at $\sin\!\left(\frac{\pi y}{b}\right)$ :