I can see some problems with what you've got.
First off one of your boundary conditions is incorrectly specified.
You say that $u(\infty,t)=0$ but you've entered it as $u(y, \infty)=0$
Second your boundary and initial conditions aren't consistent at (0,0).
One boundary condition says $u(0,0)=c$ the initial condition says $u(0,0)=0$