Toronto Math Forum
APM3462012 => APM346 Math => Misc Math => Topic started by: Kun Guo on November 14, 2012, 10:41:56 PM

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?

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?
Your observation here is wrong and solutions are correct $X_0(t)T_0(t)= \cos(x/2) e^{\frac{1}{2}t}$ satisfies boundary conditions.

Yes I got X0(t)T0(t)=cos(1/2*x)*exp(1/2*t). But one solutions posted last year have either 0 or pi/2...

Yes I got X0(t)T0(t)=cos(1/2*x)*exp(1/2*t). But one solutions posted last year have either 0 or pi/2...
So what? Someone posted a wrong solution.