Differential Equations and Linear Algebra (4th Edition)

$y=\frac{x^{n+2}}{(n+1)(n+2)}+C_1x+C_2$, valid for all values.
Integrate the function to turn $y''$ into $y'$. Don't forget integration constants. $$y''=x^n$$ $$y'=\frac{x^{n+1}}{n+1}+C_1$$ Integrate once again to turn $y'$ to $y$. $$y=\frac{x^{n+2}}{(n+1)(n+2)}+C_1x+C_2$$ This solution is valid for all values.