Quasilinear Differential Equation/Examples/x + y y' = 0/Proof 1

Proof
Let us rearrange the equation in question:

This is in the form:
 * $y \rd y = k x \rd x$

where $k = 1$.

From First Order ODE: $y \rd y = k x \rd x$:


 * $y^2 = \paren {-1} x^2 + C$

from which the result follows.