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/1841209 – 2016-06-29
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[1841209] Clairaut's form of $(x\frac{dy}{dx}-y)(y\frac{dy}{dx}+x)=a^2\frac{dy}{dx}$