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

Theorem
The first order quasilinear ordinary differential equation over the real numbers $\R$:
 * $x + y y' = 0$

has the general solution:
 * $x^2 + y^2 = C$

where:
 * $C > 0$
 * $y \ne 0$
 * $x < \size {\sqrt C}$

with the singular point:
 * $x = y = 0$