Chapter 8.7, Problem 21E

To determine

(a)

To show:

The given equation in the form,

$\frac{{\partial }^{2}y}{\partial t^2}+\frac{2}{t}\frac{dy}{dt}+{\alpha }^{2}y=0$, $t>0$.

To determine

(b)

To find:

At least first six non zero terms in the series expansion about $t=0$ for a general solution to the equation obtained in part (a).

To determine

(c)

To find:

An expansion about $x=\infty$ for a general solution using part(b).