Chapter 5.6, Problem 21P

(a)

To determine

To show: That the point $x=0$ an irregular singular point if $s>1\text{ or }t>2$.

(b)

To determine

A solution of the given differential equation of the form of $y={\displaystyle \sum _{n=0}^{\infty }{a}_n{x}^{r+n}},x>0$.

(c)

To determine

To show: That there are no solutions at $s=1,t=3$.

(d)

To determine

To show: That the maximum value of s and t for indicial equation is quadratic are $s=1,t=2$.