What is the general solution of $\frac{dy}{dx} = \frac{y}{x} + \tan\frac{y}{x}$?

Explanation

1. 01

   $y = vx$: $v + x\frac{dv}{dx} = v + \tan v$, so $\cot v\,dv = \frac{dx}{x}$.

2. 02

   $\log\lvert \sin v \rvert = \log\lvert x \rvert + c$, so $\sin\frac{y}{x} = Cx$.