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**Lancet** I've got a linear 1st order ODE, which I'm trying to solve via integrating factors:

$\displaystyle \frac{dy}{dx} = 3 - 6x + y - 2xy$

Book Answer:

$\displaystyle y = -3 + ce^{x^2 - x}$

So, from here, this is what I start out with:

$\displaystyle \frac{dy}{dx} + y(-1 + 2x) = 3 - 6x$

$\displaystyle P(t) = 2x -1$

$\displaystyle U = e^{\int 2x - 1 dx} = e^{x^2 - x}$

$\displaystyle \int \frac{d}{dx}[ye^{x^2 - x}] = \int 3e^{x^2 - x} - 6xe^{x^2 - x} dx$

But working from here would seem to require integrating $\displaystyle e^{x^2 - x}$, which I didn't think was trivially doable.

Where am I going wrong?