(a) Find two power series solutions for y xy y 0 and express the solutions y1(x) and

Chapter 6, Problem 29

(choose chapter or problem)

(a) Find two power series solutions for y xy y 0 and express the solutions y1(x) and y2(x) in terms of summation notation. (b) Use a CAS to graph the partial sums SN(x) for y1(x). Use N 2, 3, 5, 6, 8, 10. Repeat using the partial sums SN(x) for y2(x). (c) Compare the graphs obtained in part (b) with the curve obtained by using a numerical solver. Use the initial-conditions y1(0) 1, y1(0) 0, and y2(0) 0, y2(0) 1. (d) Reexamine the solution y1(x) in part (a). Express this series as an elementary function. Then use (5) of Section 4.2 to find a second solution of the equation. Verify that this second solution is the same as the power series solution y2(x). 3