# Math Help - 1st order linear equation with integral can not figure out

1. ## 1st order linear equation with integral can not figure out

Problem statement: Find the general solution of the given differential equation:

$y' + 2*xy = {x}^{3}$

Using P(x) = 2*x, I obtained an integration factor of ${e}^{{x}^{2}}$

$\frac{d}{dx} ( {e}^{{x}^{2}} * y) = {e}^{{x}^{2}}*{x}^{3}$

My question is would it be okay in this instance to leave the integral of $\int {e}^{{x}^{2}}*{x}^{3} dx$ as my answer? Or have I approached the problem incorrectly?

2. You can integrate your integral. Let $u = x^2$ so $du = 2x dx$ and your integrate becomes

$\dfrac{1}{2} \int u e^udu$ which can be integrated by parts.

3. Thanks a bunch. I have been trying to figure this thing out for days. The most obvious stuff sometimes escapes me.