Question: 1. Solve the boundary-value problem y + x y' - 4xy = 2x3+6x2 -2, y(0) =0, y(1) = 2 by using the shooting method. Use

1. Solve the boundary-value problem y" + x y' - 4xy = 2x3+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 = x4 - x2 + 2x

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