Originally Posted by

**jameselmore91** I'm starting on non-linear differential equations and there was a particular example in the book which didn't make much sense to me. It is as follows:

Solve the differential equation

$\displaystyle \left( x^{2}\; -\; 1 \right)p^{2}\; -\; 2xyp\; +\; y^{2}\; -\; 1\; =\; 0$

They rewrite the equation in this form:

$\displaystyle \left( y\; -\; xp \right)^{2}\; -\; 1\; -\; p^{2}\; =\; 0$

And the say that it "could be broken into two equations, each of Clairaut's form." This assumption confuses me. What is the logic behind it?

oh yeah! $\displaystyle p\; =\; \frac{dy}{dx}$