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Math Help - An ode

  1. #1
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    An ode

    Is there an easy way to solve the ODE

     <br />
\dfrac{dy}{dx} = \dfrac{2y^3\left(x-y-xy\right)}{x\left(x-y)^2}<br />
?
    Last edited by Jester; January 9th 2011 at 08:41 AM.
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  2. #2
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    I have a dumb answer, Mathematica, MatLab, or Maple.
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  3. #3
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    I don't know about Mathematica or Matlab but Maple readily spits out the answer. I was really looking for a non-CAS method.
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  4. #4
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    Quote Originally Posted by Danny View Post
    I don't know about Mathematica or Matlab but Maple readily spits out the answer. I was really looking for a non-CAS method.
    I figured as much but that was my answer for an easy way to do it.
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  5. #5
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    Danny, check if a substitution or variable change like this would solve your problem.

     <br />
z=\dfrac{1}{y}-\dfrac{1}{x}<br />


    Quote Originally Posted by Danny View Post
    Is there an easy way to solve the ODE

     <br />
\dfrac{dy}{dx} = \dfrac{2y^3\left(x-y-xy\right)}{x\left(x-y)^2}<br />
?
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  6. #6
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    Please allow me to ask the motivation for such a substitution?
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