In problem repeat the indicated problem using the RK4 method. First use h = 0.2 and then use h = 0.1.

Problem 2

Use Euler’s method to approximate y(1.2), where y(x) is the solution of the initial-value problem

x² y'' - 2xy' + 2y = 0, y(1) = 4, y'(1) = 9,

where x > 0. Use h = 0.1. Find the analytic solution of the problem, and compare the actual value of y(1.2) with y₂.