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Math Help - calculus first order differential equation~

  1. #1
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    calculus first order differential equation~

    could i get some help solving the DE's

    y' = (-2/x)y + (x^2)(e^x)

    thank you where y(1) = (sqrt(2))e
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  2. #2
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    Quote Originally Posted by pandakrap View Post
    could i get some help solving the DE's

    y' = (-2/x)y + (x^2)(e^x)

    thank you where y(1) = (sqrt(2))e

    This can be solve using an integrating factor

    y'+\frac{2}{x}y=x^2e^{x}

    I(x)=e^{\int \frac{2}{x}dx}=e^{\ln(x^2)}=x^2

    So if we multiply the equation by the integrating factor we get

    x^2y'+2xy=x^4e^{x} \iff \frac{d}{dx}\left( x^2y\right)=x^4e^{x}

    you now just need to integrate both sides and solve for y.

    The right hand side will be integration by parts 4 times.

    Good luck.
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    you are my life savor man, thanks so much
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