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how to solve this equation:

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

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

and $h$ is a constant.

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    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.2011-05-03
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    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?2011-05-03
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    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?2011-05-03
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    @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.2011-05-03
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    @All:thanks, what a bad mistake :D. Q EDITED.2011-05-03
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    Doman: To quote Hans Lundmark, *what is your question, exactly?*2011-05-03
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    Similar to http://math.stackexchange.com/questions/18412092016-06-29

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