Quasilinear Differential Equation/Examples/x + y y' = 0/Proof 2

Proof
Observe that from Derivative of Power and Chain Rule for Derivatives:
 * $\dfrac {\map \d {x^2 + y^2} } {\d y} = 2 x + 2 y \dfrac {\d y} {\d x}$

Hence:
 * $\dfrac {\map \d {x^2 + y^2} } {\d y} = 0$

So from Derivative of Constant:
 * $x^2 + y^2 = C$

where $C$ is abitrary.