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.

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

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