Differential equation $y' = -2x y+ e^{-x^2}\sin(x)$ Can someone help me solve this equation?
$$y' = -2xy + e^{-x^2}\sin(x)$$
Progress
I have been trying to solve it with the method of integrating factor.  I get to the point where:  $$y'+2xy=e^{-x^2}\sin(x)$$ Then I multiply each with: $e^{x^2}$. So I'm left with
$$e^{x^2}y  = \int  e^{x^2} \sin(x)$$
But from here I'm not sure how I can integrate.

When you multiply both sides of $y' + 2xy = e^{-x^2}\sin x$ by $e^{x^2}$, you should have gotten: 
$e^{x^2}y' + 2xe^{x^2}y = \sin x$
$\dfrac{d}{dx}[e^{x^2}y] = \sin x$
(Note that the right hand side is $\sin x$ and not $e^{x^2}\sin x$.)
Fortunately, you can write the antiderivative of $\sin x$ without using the error function. 
