(a) The differential equation x4 y ly 0 has an irregular singular point at x 0. Show
Chapter 5, Problem 33(choose chapter or problem)
(a) The differential equation \(x^{4} y^{\prime \prime}+\lambda y=0\) has an irregular singular point at x=0. Show that the substitution t=1/x yields the differential equation
\(\frac{d^{2} y}{d t^{2}}+\frac{2}{t} \frac{d y}{d t}+\lambda y=0\)
which now has a regular singular point at t=0.
(b) Use the method of this section to find two series solutions of the second equation in part (a) about the singular point t=0.
(c) Express each series solution of the original equation in terms of elementary functions.
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