Question

The differential equation of the family of curves represented by the equation $x^{2}y=a$, is

• A. $\frac{dy}{dx}+\frac{2y}{x}=0$
• B. $\frac{dy}{dx}+\frac{2x}{y}=0$
• C. $\frac{dy}{dx}-\frac{2y}{x}=0$
• D. $\frac{dy}{dx}-\frac{2y}{y}=0$

Answer 1

The correct option is A

$\frac{dy}{dx}+\frac{2y}{x}=0$

$x^{2}y=a$ (On differentiating)
$x^2\frac{dy}{dx}+y\frac{d}{dx}\left(x^2\right)=0\Rightarrow x^2\frac{dy}{dx}+2xy=0\Rightarrow \frac{dy}{dx}+\frac{2y}{x}=0.$