I need to solve the equation:
${\partial^2 T(x,t) \over \partial x^2 }= {1 \over \alpha} {\partial T(x,t) \over \partial t}$
With the boundary conditions
$T(0,t)=T_0$ and ${\partial T(L,t) \over \partial x}=-q_L \alpha$
Subject to the initial condition
$T(x,0)=T_i(x)$
I tried to do it by separation of variables and I arrived at a solution but I can not get to propose the general solution