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

Theorem
The linear first order ODE:
 * $\dfrac {\mathrm d y} {\mathrm d x} + \dfrac y x = 3 x$

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

or:
 * $y = x^2 + \dfrac C x$

Proof
This is a special case of:
 * Linear First Order ODE: $\dfrac {\mathrm d y} {\mathrm d x} + \dfrac y x = k x^n$

where $k = 3$ and $n = 1$, yielding:
 * $y = x^2 + \dfrac C x$

Multiplying through by $x$ reveals:
 * $x y = x^3 + C$