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