In: Advanced Math
For each problem (A and B),
- Seek power series solutions of the given differential equation about the given point x0 and find the recurrence relation.
- Find the first four terms in each of two solutions y1 and y2 (unless the series terminates sooner).
- By evaluating the Wronskian W(y1, y2)(x0), show that y1 and y2 form a fundamental set of solutions.
- If possible, find the general term in each solution.
A) (1 - x)y" + y = 0; x0 = 0
B) xy" + y' + xy = 0; x0 = 1