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Math Help - Integral help

  1. #1
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    Integral help

    Hi.

    This is a differential equation but im stuck at the integral.

    dy/dx + 2xy = xy^2 + 2x

    i moved everything to one side except y' and factored out x. I get:

    dy/dx = x(y^2 - 2y +2)

    then

    dy/(y^2 - 2y +2) = x dx

    how do i integrate the left side?
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  2. #2
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    Quote Originally Posted by Kuma View Post
    dy/(y^2 - 2y +2) = x dx
    how do i integrate the left side?
    y^2-2y+1=(y-1)^2+1
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  3. #3
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    y^2-2y+2 = (y^2-2y+1)+1 = (y-1)^2+1,
    so \int\frac{1}{y^2-2y+1}\;{dy} = \int\frac{1}{(y-1)^2+1}\;{dy}. Now, let t = (y-1).
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