Frobenius method for fourth order linear ODE

[eradi]

By using frobenius method I find the roots of the indicial equation of a 4th order ODE to be
0, 1, 1, 2
Now, what is the form of the corresponding series solution of this equation with log terms?

 

[HallsofIvy]

You should be looking for a solution to the form
$$\sum a_nx^n+ \sum b_nx^{n-1}+ log(x)\sum c_n x^{n-1}+ \sum d_n x^{n-2}$$

 

[eradi]

no matter about the condition that the roots differ by integers?