Solving 3xy" - 4y' - xy = 0 with Frobenius

[glitchy]

I'm really getting stuck at this and I'm trying to read on it but it's confusing.

I need just a start-up for this equation which is to be solved with the method of frobenius.

3xy" - 4y' - xy = 0

Just need a start.

Any help is appreciated.

Thank you

 

[Dick]

Start by substituting a power series in x for y. y=sum(a_k*x^k). Do the derivatives and equate coefficients of equal powers. Go!

 

[glitchy]

done, then