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Math Help - differential equation

  1. #1
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    differential equation

    solve the differential equation:

    x*y*(dy/dx) = 3x^2 + y^2

    i have real problems with differential equations so if anyone could give a brief method or some reasoning id really appreciate it. Thanks
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  2. #2
    Super Member Matt Westwood's Avatar
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    If you express it in the form

    dy / dx + ay = f(x)

    you can use the integrating factor method.
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  3. #3
    Super Member wingless's Avatar
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    Arrow

    Quote Originally Posted by snowmonkey12 View Post
    solve the differential equation:

    x*y*(dy/dx) = 3x^2 + y^2
    x y y' = 3x^2 + y^2
    y' = (3x^2 + y^2) / (x y)
    y' = 3x/y + y/x
    y' - y/x = 3x/y
    (x y' - y) / x = 3x/y
    (y/x)' x = 3x/y
    (y/x)' = 3/y
    Let y = u x ,
    u' = 3 / (u x)
    u du = 3 dx / x
    u^2 = 6 ln |x| + 2C
    y^2 = 6 x^2 ln |x| + 2 C x^2
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  4. #4
    Super Member Matt Westwood's Avatar
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    Oh of course, yes. It's homogeneous. Sorry for my previous posting. It was rubbish.
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