This is a form of Euler Equation:

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I'll show you how to find the homogeneous solution. and you'll go from there:

The trick is to use the following substitution:

thus :

after substituting these results into the ode we get a regular constant coefficients ODE:

the characteristic polynomial is:

so the general solution is:

or in terms of x:

now you can find the particular solution using the method of variation of parameters...

[The latex came kinda massed up, don't know how to fix it]