Consider the square cross section of a long solid bar as shown in the diagram below.

$T(x,L)=T_{1}sin(2\frac{x}{L})$

For the coordinate system shown in the figure, the temperature distributions on the

boundaries are $T(x,0)=T_0,T(0,y)=T_0,T(x,L)=T_{1}sin(2\frac{x}{L}),$ and $T(L,y)=$

$T_{1}sin(3\frac{y}{L}),$ where $T_0$ and $T_1$ are constants. Find an expression for the temperature

distribution $T(x,y)$ in this solid.