$2\mathrm{.}3.$ Use the method of separation of variables to solve $($at least formally$)$ the following mixed problem:

$u_t-D{u}_{}=0,00$

$u(x,0)=g(x),0x$

$u_x(0,t)=0,t>0.$

$u_x(L,t)+u(L,t)=U,$

$[$Answer: $u(x,t)={\displaystyle \underset{k0}{\overset{?}{}}}{c}_k{e}^{-D{}_k^{2}t}cos{}_{k}x,$ where the numbers ${}_k$ are the positive solutions of the equation $tan=1.$