Chapter 8.6, Problem 44E

To determine

(a)

To show:

Coefficients $a_k$ $k\ge 1$ of the series solution of the given differential equation, satisfy the given recurrence relation.

To determine

(b)

To find:

The second series solution with $r=\frac{1}{2}$ in the recurrence relation in part a.

To determine

(c)

To find:

$w\left(1,x\right)$ using the recurrence relation in part a with $r=1$.