Moderate# Series Solutions for Nonlinear Equations

DIFFEQ-JRXHSX

Consider the equation $y'=1+x-y^2$. This is nonlinear equation but we may also pursue power series solution near $x=0$ by trying the ansatz $y=\sum_{n=0}^{\infty}a_nx^n$.

Then, $a_0, a_1, a_2,a_3$ for the solution satisfying $y(0)=1$ are equal to: