Question

(a) Seek power series solutions of the given differential equation about the given point x0;
find the recurrence relation.
(b) Find the first four terms in each of two solutions y1 and y2 (unless the series terminates
sooner).
(c) By evaluating the Wronskian W(y1, y2)(x0), show that y1 and y2 form a fundamental set
of solutions.
(d) If possible, find the general term in each solution.

1. y''-y=0, x0=0

2. y''-xy'-y=0, x0=0

3. (4-x^2)y''+2y=0, x0=0

4. 2y''+(x+1)y'+3y=0, x0=2

Answer 1