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)

A family of circles whose centres are on the x-axis

$ydy=(c-x)dx$

$\int ydy=\int (c-x)dx$

$\frac{y^2}{2}=cx-\frac{x^2}{2}+k$

$\frac{x^2}{2}+\frac{y^2}{2}-cx=k$

$x^2+y^2-2cx=2k$

$(x-c{)}^2+y^2=2k+c^2$

This is equation of a circle with center on x-axis.

(d)