Which exactly is missing in the exercise?

Solve the following PDE (Partial Differential Equations) problem: u C(R (0,00)) n C(R[0,00)) U = U22 + H (x)e-t in RX (0,00), u(x,0) = 0 in R, where Ho(a) = { + se 2 b for b>0. What are the Eigenfunctions (n) if we consider the following candidate solution for the problem set above? u(x, t) = n(t), (2) n=1 Solve the following PDE (Partial Differential Equations) problem: u C(R (0,00)) n C(R[0,00)) U = U22 + H (x)e-t in RX (0,00), u(x,0) = 0 in R, where Ho(a) = { + se 2 b for b>0. What are the Eigenfunctions (n) if we consider the following candidate solution for the problem set above? u(x, t) = n(t), (2) n=1