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Math Help - Diff. Equation's General Formula use Substitution

  1. #1
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    Diff. Equation's General Formula use Substitution

    I'm really stomped with this problem... i can't seem to get the answer...

    anyway... here's the problem..

    (2(x^3) - (y^3))y'=3(x^2)y

    and i need to get the general solution....

    SO, here's what i did...

    I Let
    u=x^3 and
    du=3x^2dx

    so what happens is

    2udy-(y^3)dy= ydu

    and that's where i got stuck...

    i tried using
    d(u/y)=(ydu-udy)/y^2

    but i can't seem to get rid of the 2 in 2udy and it would be much of a problem if i did that...

    could anyone help me??
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  2. #2
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    Quote Originally Posted by asteg123 View Post
    I'm really stomped with this problem... i can't seem to get the answer...

    anyway... here's the problem..

    (2(x^3) - (y^3))y'=3(x^2)y
    What we have is,
    y'=\frac{3x^2y}{2x^3-y^3}
    This is a homogenous equation which can be transformed into a seperate equation.
    If you use the substitution,
    y=vx<----> y/x=v
    Then,
    y'=v+v'x
    If you divide by the numerator and denominator you have,
    y'=\frac{3}{2(x/y)-(y/x)^2}
    Thus,
    v+v'x=\frac{3}{\frac{2}{v}-v^2}
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