The differential equation $y\frac{{dy}}{{dx}} + x = C$ represents

Given that, $y\frac{{dy}}{{dx}} + x = C$

$\Rightarrow$ $y\frac{{dy}}{{dx}} = C - x$

$\Rightarrow$ $ydy = (C - x)dx$

On integrating both sides,

we get
$\frac{{{y^2}}}{2} = Cx - \frac{{{x^2}}}{2} + K$

$\Rightarrow$ $\frac{{{x^2}}}{2} + \frac{{{y^2}}}{2} = Cx + K$

$\Rightarrow$ $\frac{{{x^2}}}{2} + \frac{{{y^2}}}{2} - Cx = K$

which represent family of circles.