Question

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

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

Answer 1

Answer: (C)

parabolas

Correct answer is $\left(C\right)$. Given equation can be written as
$\frac{2dy}{y+3}=\frac{dx}{x}\Rightarrow 2\log (y+3)=\log x+\log c$
$\Rightarrow (y+3{)}^2=cx$ which represents the family of parabolas.