Question

The D.E whose solution is $y=c{x}^2$ is

• A. $2y=x^2\frac{dy}{dx}$
• B. $y=2x\frac{dy}{dx}$
• C. $2y=x\frac{dy}{dx}$
• D. $y=x^2\frac{dy}{dx}$

Answer 1

Answer: (C)

$y=c{x}^2\dots \left(1\right)$
$\Rightarrow \frac{dy}{dx}=2cx$
$\Rightarrow \frac{dy}{dx}=2\left(\frac{y}{x^2}\right)x\because$ from $\left(1\right)$
$\Rightarrow x\frac{dy}{dx}=2y$