Question

If $\frac{dy}{dx}+\frac{2y}{x}=0,y(1)=1$, then $y(2)$ is equal to

• A. 1
• B. 2
• C. 4
• D. $\frac{1}{4}$

Answer 1

Answer: (D)

We have $\frac{dy}{y}=-2\frac{dx}{x}$
$\Rightarrow \ln y=-2\ln x+C$
As $y(1)=1\Rightarrow C=0$
So, $y=\frac{1}{x^2}\Rightarrow y(2)=\frac{1}{4}$.