Question

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

• A. a family of hyperbolas
• B. a family of circles whose centres are on the y-axis
• C. a family of parabolas
• D. a family of circles whose centres are on the x-axis

Answer 1

Answer: (D)

Given differential equation is
$y \frac{d y}{d x}+x=c$
$\Rightarrow \,\,\,\,\,\,y \,d y=(c-x) d x$
On integrating both sides, we get
$\frac{y^{2}}{2}=c x-\frac{x^{2}}{2}+d$
$\Rightarrow \,\,\,\,\,\, y^{2}+x^{2}-2 c x-2 d=0$
Hence, it represents a family of circles whose centres are on the $x$ -axis.