An ode

**Danny** · January 9th 2011, 08:17 AM

Is there an easy way to solve the ODE

$ \dfrac{dy}{dx} = \dfrac{2y^3\left(x-y-xy\right)}{x\left(x-y)^2} $ ?

**dwsmith** · January 9th 2011, 02:20 PM

I have a dumb answer, Mathematica, MatLab, or Maple.

**Danny** · January 9th 2011, 03:09 PM

I don't know about Mathematica or Matlab but Maple readily spits out the answer. I was really looking for a non-CAS method.

**dwsmith** · January 9th 2011, 03:10 PM

Originally Posted by Danny

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.

**carrot** · January 10th 2011, 02:43 PM

Danny, check if a substitution or variable change like this would solve your problem.

$ z=\dfrac{1}{y}-\dfrac{1}{x} $

Originally Posted by Danny

Is there an easy way to solve the ODE

$ \dfrac{dy}{dx} = \dfrac{2y^3\left(x-y-xy\right)}{x\left(x-y)^2} $ ?

**Danny** · January 10th 2011, 03:45 PM

Please allow me to ask the motivation for such a substitution?

Thread: An ode