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

Explanation

1. 01

   $y = vx$: $v + x\frac{dv}{dx} = 1 + v$, so $\frac{dv}{dx} = \frac{1}{x}$.

2. 02

   $v = \log\lvert x \rvert + C$, so $y = x\log\lvert x \rvert + Cx$.