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  4. If (d y/d x)+(2 y/x)=0, y(1)=1, then y(2) is equal to

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

Differential Equations

Solution:

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