Question

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

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

Answer 1

Answer: (A)

a set of circles whose centres are on the x-axis

$y\frac{dy}{dx}+x=a$

$2y\frac{dy}{dx}+2x=2a$

$\frac{d}{dx}{y}^2+\frac{d}{dx}{x}^2=2a$

$\Rightarrow \frac{d}{dx}(x^2+y^2)=2a$

$\Rightarrow x^2+y^2=2ax+c^2$

$\Rightarrow (x-a{)}^2+y^2=c^2$