# Math Help - An ode

1. ## An ode

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}
$
?

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

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

4. 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.

5. 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}
$
?

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