Question

The solution of differential equation $2x\frac{dy}{dx}-y=3$ represents a family of

• A. circles
• B. straight lines
• C. ellipses
• D. parabola

Answer 1

Answer: (D)

We have,
$2x\frac{dy}{dx}=y+3$
$\Rightarrow \frac{2}{y+3}dy=\frac{dx}{x}$
integrating, $2\ln (y+3)$
$=\ln x+\ln c=\ln cx$
$\Rightarrow \ln (y+3{)}^2=\ln cx$
$\Rightarrow (y+3{)}^2=cx$
which is a family of parabolas.