Linear First Order ODE/y' - (y over x) = 3 x

Theorem
The linear first order ODE:
 * $(1): \quad \dfrac {\mathrm d y} {\mathrm d x} - \dfrac y x = 3 x$

has the solution:
 * $\dfrac y x = 3 x + C$

or:
 * $y = 3 x^2 + C x$

Proof
This is an instance of Linear First Order ODE: $y' - \dfrac y x = k x$.

Its solution is:
 * $\dfrac y x = k x + C$

or:
 * $y = k x^2 + C x$

from which the solution to $(1)$ is found by substituting $3$ for $k$.