1. Solve the boundary-value problem y" +xy 4xy = 22% + 6x2 2, y(0) = 0, y(1) = 2 by using the shooting method. Use the modified Euler method (with only one correction at each step), and take h = 0.2. Start with an initial slope of y(0) = 1.9 as a first attempt and y(0) = 2.1 as a second attempt. Then interpolate. Compare the result with the analytical solution y= 24 2? + 21. 2. Consider the following boundary-value problem: Y" = 2:2%y + xy +2, 1