Find the particular solution of the differential equation `xcos(y/x)(dy)/(dx)=ycos(y/x)+x\ ` given that when `x=1,\ y=pi/4dot`

Explanation

The given D.E. is:
$$ x \cos \left(\frac{y}{x}\right) \frac{d y}{d x}=y \cos \left(\frac{y}{x}\right)+x \text {...(i) } $$When, `quad x=1, y=\frac{\pi}{4}`
$$ \cos \left(\frac{y}{x}\right) \frac{d y}{d x}=\frac{y}{x} \cos \left(\frac{y}{x}\right)+1 \ldots \text { (ii) } $$
\begin{aligned} \text { Put, } & \frac{y}{x}=v \\ \text { or } & \frac{d y}{d x}=v+x \frac{d v}{d x} \end{aligned}$$
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