Is there a simple solution to this (ordinary) differential equation?

Question

I'm trying to solve the following differential equation:

$$ \frac{dy}{dx} = - \frac{3x + 2y}{2y}. $$

It looks pretty simple, yet it's not separable, linear, or exact. It is of the form

$$ \frac{dy}{dx} = f(y/x). $$

I could do the substitution $v = y/x$, and I know it would look pretty ugly, but is there a better or simpler method?

Answer 1

One way I can think is to solve: $$ \frac{dy}{dt} = -3 x - 2y \\ \frac{dx}{dt} = 2 y $$ say by matrix exponentiation. Then one can invert $ x(t) $ to find $ y(x) $.