Apply separation of variables Method to solve heat equation \[u_t=3u_{xx} , 0<x0\] Boundary conditions \[u\left(0,t\right)=0, u\left(2,\ t\right)=0 for \ all t>0\] Initial condition \[u\left(x, 0\right)=sin^3{\left(\pi x\right)}=\frac{\left(3\sin{\left(\pi x\right)}-\sin{\left(3\pi x\right)}\right)}{4} for 0\le x\le2\]
SK Math Expert Changed status to publish June 20, 2022