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

  1. #1
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    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?
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  2. #2
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    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.
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  3. #3
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    Thanks a bunch. I have been trying to figure this thing out for days. The most obvious stuff sometimes escapes me.
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