I've made a lot of simplifications to a Joule-heating problem I'm working on. I'm struggling to solve the following one-dimensional, one variable ODE: Txx + aT = -b with boundary conditions T(x=0) = Ts (Dirichlet) Tx(x=L) = 0 (Neumann) I've learned that this is a non-homogeneous ODE with non-homogenous boundaries. I've tried using FDM to solve them and then fitting the data to a function, but I didn't get far. I would love some help on this. I have much more experience with numerical analysis than analytical. I really need a math-wiz's help.