Chapter 5.2, Problem 3P

(a)

To determine

To seek: A power series solution for the differential equation $y^{″}-x{y}^{\prime }-y=0$ about the point $x_0=0$ and obtain the recurrence relation.

(b)

To determine

The first four terms for the two solutions of $y_1\text{ and }{y}_2$.

(c)

To determine

To show: The expression of $y_1\text{ and }{y}_2$ form a fundamental set of solution by evaluating Wronskian $W_{\left(y_1,y_2\right)}\left(x_0\right)$.

(d)

To determine

The general term of each solution if possible.