find solution of heat equation ut=3uxx with Dirichlet boundary conditions Solution : \[u_t=3u_{xx}\ ,\ 0<x<2\ ,\ t>0\] (1) Boundary conditions \[u\left(0,\ t\right)=0,\ \ u\left(2,\ t\right)=0\ \ \ for\ all\ t>0 \] (2) 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}…
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