Verifying Heat Equation in Metal Rod: Help Needed!

[foranlogan2]

can anyone help me interpret what exactly this question is asking as i am quite unawares

By direct substitution into the heat equation and calculation of boundary values,
verify that the solution u(x, t) for a metal rod of length L which satisfies
the initial temperature u(x, 0) = f(x) and the boundary conditions
u(0, t) = u(L, t) = 0 is given by

u(x, t) = (sum)B(n)sin(npix/L)Dx

NB: Do not re-derive this formula, just verify that it satisfies the equation and
boundary conditions!]

i don't know how to do this without rederiving this equation,i do not know how to answer this question ,could anyone help
thanks

 

[mjsd]

ie. put your given solution into the equation and show that LHS =RHS