Use the Linear Shooting method to approximate the solution to the following boundary-value problems.
a. y" = −3y' + 2y + 2x + 3, 0 ≤ x ≤ 1, y(0) = 2, y(1) = 1; use h = 0.1.
b. y" = −4x−1y' − 2x−2y + 2x−2 ln x, 1≤ x ≤ 2, y(1) = −1 / 2 , y(2) = ln 2; use h = 0.05.
c. y" = −(x + 1)y' + 2y + (1 − x2)e−x, 0≤ x ≤ 1, y(0) = −1, y(1) = 0; use h = 0.1.
d. y" = x−1y' + 3x−2y + x−1 ln x−1, 1 ≤ x ≤ 2, y(1) = y(2) = 0; use h = 0.1.