# A differential equation (nonlinear First-Order)

how to solve this equation:

$(Px-y)(Py+x)=h^2P$

that $P=\frac{dy}{dx}$

and $h$ is a constant.

-
Typically, one tries to find an integrating factor... Your equation looks a bit suspicious. Is it homework/exercise in a book? Did you copy the problem correctly? As it is stated it is not a second order DE, but a (quite nonlinear) first order DE. –  Fabian May 3 '11 at 7:12
this is a homework,i say "I know it gets First Order" because our lesson treat on FO DE :D,its equal to : $xyP^2+(x^2-y^2-h^2)P-xy=0$, can help? –  Doman May 3 '11 at 7:23
It's a first order ODE, since it involves $y(x)$ and the first derivative $y'(x)$. (Not higher derivatives like $y''(x)$ etc.) What's your question, exactly? –  Hans Lundmark May 3 '11 at 7:42
@Doman: even when there is $P^2$ it is still a first order ODE (no $y''(x)$ appearing). It is just a nonlinear differential equation. –  Fabian May 3 '11 at 7:55
@All:thanks, what a bad mistake :D. Q EDITED. –  Doman May 3 '11 at 14:01