utâˆ’kuxx=0 for xâˆˆ(0,Ï€)

with the boundary conditions ux(0,t)=0 and u(Ï€,t)=0 and the initial condition u(x,0)=x.

Part d) Write the solution in the form of a series.

If we use separation of variables, U=X*T, I found that T0 is t dependent. Then A0*T0 cannot not just a constant or zeor(A0 is for X).

Are there any mistakes regarding that part in both solutions poster last year?