Del u$/$ del t $=$ del$^2$ u$/$ del x$^2+2/$x $*$ del u$/$ del x $,0<=$x$<=1,$ t$>0.$ Initial condition u $=1-$ x$^2,$ t$=0$

Boundary condition del u$/$ del x $=0$ at x$=0$ and u$=0$ at x$=1$

solve it