# An ode

• Jan 9th 2011, 08:17 AM
Jester
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}
$
?
• Jan 9th 2011, 02:20 PM
dwsmith
I have a dumb answer, Mathematica, MatLab, or Maple.
• Jan 9th 2011, 03:09 PM
Jester
I don't know about Mathematica or Matlab but Maple readily spits out the answer. I was really looking for a non-CAS method.
• Jan 9th 2011, 03:10 PM
dwsmith
Quote:

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.
• Jan 10th 2011, 02:43 PM
carrot
Danny, check if a substitution or variable change like this would solve your problem.

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

Quote:

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}
$
?

• Jan 10th 2011, 03:45 PM
Jester