Question

The solution of the differential equation $2x\frac{dy}{dx}=y;y\left(1\right)=2$ represents $=$ ____.

• A. parabola
• B. ellipse
• C. circle
• D. line

Answer 1

Answer: (A)

parabola

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

$⟹2\frac{dy}{y}=\frac{dx}{x}$

Integrating both sides-

$2\log y=\log x+c$

For $y\left(1\right)=2-$

$2\log 2=\log 1+c⟹c=2\log 2$

Hence,

$2\log y=\log x+2\log 2$

$⟹\log y^2=\log 4x$

$⟹y^2=4x$

This is the equation of parabola.