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Math Help - dy/dx= x / (x^2y+y^3)

  1. #1
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    dy/dx= x / (x^2y+y^3)

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

    its been a while since I had diff eq and this problem came up, could i get some help please?
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  2. #2
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    Re: dy/dx= x / (x^2y+y^3)

    What methods do you know on how to solve DEs?
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    Re: dy/dx= x / (x^2y+y^3)

    I know i need to separate and integrate, but i cant quite figure out how. I know there is probably some substitution in there but I'm not getting it
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    MHF Contributor chisigma's Avatar
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    Re: dy/dx= x / (x^2y+y^3)

    Quote Originally Posted by firestar928 View Post
    dy/dx= x / (x^2y+y^3)

    its been a while since I had diff eq and this problem came up, could i get some help please?
    Writing the DE in different way, changing the role of x and y, You obtain...

    \frac{d x}{dy} = x\ y + \frac{y^{3}}{x} (1)

    ... which is 'Bernoulli type'. The solving procedure is illustrated in...


    Bernoulli Differential Equation -- from Wolfram MathWorld

    It is remarkable the fact that a Bernoulli equation has standard form...

    x^{'} + p(y)\ x = q(y)\ x^{n} (2)

    ... and the solving procedure is valid also when n is a negative number like in this case [n=-1...]

    Kind regards

    \chi \sigma
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    MHF Contributor FernandoRevilla's Avatar
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    Re: dy/dx= x / (x^2y+y^3)

    Another way: the equation has an integrating factor \mu=\mu(y) that depends on y .
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