Am not sure how helpful this will be but the problem is of the type Cauchy-Euler

Cauchy

This will at leat give you something to look up.

I will also give two ideas:

Idea 1: Solve the homogenous problem first.

Now find the particular solution by guessing it is a Monomial of degree 3. (do you see what it cannot have any lower degree terms.)

Idea 2

Let

Then

This will transform the equation into

This is a first order linear differential equation with contant coeffiencts.

Just FYI the usual "guess" is