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)

parabola

Answer 2

The correct option is (D): parabola
As we have, $2 x \frac{d y}{d x}=y+3$
$\Rightarrow \frac{2}{y+3} d y=\frac{d x}{x}$
integrating, $2 \ln (y+3)$
$=\ln x+\ln c=\ln c x$
$\Rightarrow \ln (y+3)^{2}=\ln c x$
$\Rightarrow(y+3)^{2}=c x$
which is a family of parabolas.