I am curious about whether one can find a series solution to the differential equation $$y’=f(y,t)+k \ \ \ \ k \in \mathbb{R}$$
I know the standard way of solving a differential equation using power series is to arrange it into the form $$\sum_{n=0}^\infty[g(a_{n+1},a_n,...)]t^n=0$$ and then find a recurrence relation. However, I am not sure if writing my above differential equation in the form $$\sum_{n=0}^\infty[g(a_{n+1},a_n,...)]t^n=k$$ Will give me a recurrence relation. Any help is appreciated.