Question

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

• A. a straight line
• B. an ellipse
• C. a parabola
• D. circles

Answer 1

The correct option is C a parabola

$2x\frac{dy}{dx}=y+3\Rightarrow \frac{dy}{dx}=\frac{y+3}{2x}\Rightarrow \frac{2\frac{dy}{dx}}{y+3}=\frac{1}{x}$
Integratin both sides
$\int \frac{2\frac{dy}{dx}}{y+3}=\int \frac{1}{x}\Rightarrow 2\log (y+3)=\log x+c\Rightarrow {(y+3)}^2=x+C$