Chapter 9.4, Problem 4E

In Problems 3 and 4 repeat the indicated problem using the RK4 method. First use h = 0.2 and then use h = 0.1.

Problem 2

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

$x^2{y}^{″}-2x{y}^{\prime }+2y=0,y\left(1\right)=4,y^{\prime }\left(1\right)=9,$

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.