CAS PROJECT. Isotherms. Find the steady$-$state solutions $($temperatures$)$ in the square plate in Fig. $297$ with $a=2$ satisfying the following boundary conditions. Graph isotherms.

$($a$)u=80sinx$ on the upper side, $0$ on the others.

$($b$)u=0$ on the vertical sides, assuming that the other sides are perfectly insulated.

$($c$)$ Boundary conditions of your choice $($such that the solution is not identically zero$).$

Fig. $291.$ square plate