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

Chapter 11, Problem 4

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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 = 4x1y 2x2y + 2x2 ln x, 1 x 2, y(1) = 1 2 , y(2) = ln 2; use h = 0.05; actual solution y(x) = 4x1 2x2 + 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 x3ex 5 3 xex + 2ex x 2. 5. Use th