Solve the following differential equation: `\ x(dy)/(dx)=y-xcos^2(y/x)`

Explanation

Given `\ x(dy)/(dx)=y-xcos^2(y/x)`



Dividing throughout by `x`

`frac{d y}{d x}=\frac{y}{x}-\cos ^{2}(\frac{y}{x})`...(1)

It is a homogeneous equation.

Put `y=v x`

And `x \frac{d v}{d x}+v=\frac{d y}{d x}`.
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