# Power series solution for nonlinear ODE

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.

• The equation is separable. Are you specifically required to find a power series solution? – John Wayland Bales Apr 20 at 6:16
• Make a substitution: let $w=y-2$ for instance. – player100 Apr 20 at 11:45
• Yes, the exercise is to solve it using power series. – Tyler6 Apr 21 at 2:28