Consider the equation $u_t = u_{xx} - 4 u$, $0 < x < 1$, $t > 0$, that is, there is a lateral heat loss. Suppose further that ends are kept as $u(0,t) = 0 , u(1,t) = 5 (e^{2}-e^{-2})$. What is the steady state solution $U(x)$, if it exists? That is, a solution after a very long time.
Hint: a steady-state solution does not depend on time.
$U(x) =$ help (formulas)