Although q(x) < 0 in the following boundary-value problems, unique solutions exist and

Chapter 11, Problem 11.1.4

(choose chapter or problem)

Although q(x) < 0 in the following boundary-value problems, unique solutions exist and are given. Use the Linear Shooting Algorithm to approximate the solutions to the following problems, and compare the results to the actual solutions. a. y + y = 0, 0 x 4 , y(0) = 1, y 4 = 1; use h = 20 ; actual solution y(x) = cos x + ( 2 1)sin x. b. y + 4y = cos x, 0 x 4 , y(0) = 0, y 4 = 0; use h = 20 ; actual solution y(x) = 1 3 cos 2x 2 6 sin 2x + 1 3 cos x. c. y = 4 x y 2 x 2 y + 2 x 2 ln x, 1 x 2, y(1) = 1 2 y(2) = ln 2; use h = 0.05; actual solution y(x) = 4 x 2 x 2 + ln x 3 2 . d. y = 2y y + xex x, 0 x 2, y(0) = 0, y(2) = 4; use h = 0.2; actual solution y(x) = 1 6 x 3ex 5 3 xex + 2ex x 2.