## Differential Equations and Linear Algebra (4th Edition)

The first order linear equation must be in the form of $y'+p(x)y=q(x)$. Therefore, the equation is rewritten as $y'-x^2y=sin(x)$. The integrating factor is equal to $e^{\int p(x) dx}$, so the integrating factor is actually $e^{-\int x^2 dx}$.