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

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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:

$x = y = 0$