I am struggling to find a series solution for the initial value problem $y’=2y^2-3y+2$, $y(0)=y_0$.
By plugging in a power series, I have simplified and gotten $$\sum_{n\ge0}[(n+1)a_{n+1}-2(a*a)_n+3a_n]=2$$where $*$ is the Cauchy product. What is giving me trouble is the constant $2$ on the side, since I do not know how to avoid it and find a recurrence relation.
Any help is much appreciated.