Diff eq, integrating factors

Question

If the question is: $x\dfrac{dy}{dx} + 6x = 3x^2$, would I begin solving by dividing everything by $x$ so that I could have a linear function?

Answer 1

Yes divide by $x$ and then take terms on right side and integrate.

Answer 2

You would indeed:

$$x\frac{dy}{dx}+6x=3x^2\implies \frac{dy}{dx}+6=3x,\quad x\neq 0$$