Show that where a, b, and c are constants, is an exact solution of both the diffusion equation and the numerical scheme, provided that the boundary conditions and the source term are adjusted to fit...

Show that

where a, b, and c are constants, is an exact solution of both the diffusion equation and the numerical scheme, provided that the boundary conditions and the source term are adjusted to fit this solution. That is, a program should compute

exactly (to machine precision).