The differential equation y (d y)/(d x)+x=C represents

We have,

$y \frac{d y}{d x}+x=C$

$\Rightarrow y d y+(x-C) d x=0$

$\Rightarrow \frac{y^2}{2}+\frac{(x-C)^2}{2}=C_1 \Rightarrow(x-C)^2+y^2=2 C_1$

Clearly, it represents a family of circles having their centres on x-axis.