ECE 6382 Homework No. 7
Due October 23, 2002
1. Consider the differential equation:
f”(x) + f(x) = 0 (equation 1)
Suppose that we have found one solution f1(x) = 1 – x2 /2! + x4/4! - …
[That is, cos(x) ].
(a) Find the differential equation for the Wronskian of solutions of equation 1.
(b) Solve the DE and obtain the solution for W.
(c) Then solve for f2(x) using the above results.
Do not use any trigonometry identity. To keep things simple, you may retain
only the first two terms of a series in all manipulations. Show that at the end,
the f2(x) series is actually sin(x) times a constant.
2. Problem 8.6.8
3. Problem 8.6.10
4. Problem 8.6.15
5. Problem 1.15.6
6. Problem 1.15.7
7. Problem 1.15.10