I'm the chapter about series and this one is about Frobenius series.

1) Find the general solution of $\displaystyle 2t^2y'' + (t^2-t)y' + y = 0$

2) Find two independent solutions of the given equation. In the problem, the roots of the indicial equation differ by a positive integer, but two solutions exist of the form $\displaystyle t^r*summation(n=0 To Infinite)a_nt^n$.

$\displaystyle t^2y'' + (3t-t^2)y' - ty = 0$

3) Find the fundamental set of $\displaystyle ty'' + (1-t^2) + 4ty = 0$