Determine the steady state temperature distribution in the semi$-$infinite metal plate shown in figure. The temperature of the two horizontal borders is kept as zero while the left boundary is $200C.$

Use Separation of Variables Method, $T(x,y)=x(x)Y(y),$ to solve the problem. Start with the $Y(y)$ part and remember that the temperature of the plate should have a finite value even at $x.(50pts$