# Solve $(1+x)y’=y$ by power series

Solve $(1+x)y’=y$ by power series. Start with $y$ and $y’$:

$y=a_0+a_1x+a_2x^2+a_3x^3+...+a_nx^n$

$y’=a_1+2a_2x+3a_3x^2+...+na_nx^{n-1}$

Then $(1+x)y’=a_1(1+x)+2a_2(1+x)x+3a_3(1+x)x^2+...+na_n(1+x)x^{n-1}$