In many of the following problems, it will be essential to have a calculator or comp...

In many of the following problems, it will be essential to have a calculator or computer available. You may use a software package† or write a program for solving initial value problems using the improved Euler’s method algorithms on pages 127 and 128. (Remember, all trigonometric calculations are done in radians.)

Use the improved Euler’s method subroutine with step size h = 0.2 to approximate the solution to the initial value problem

at the points x _ 1.2, 1.4, 1.6, and 1.8. (Thus, input N = 4) Compare these approximations with those

obtained using Euler’s method (see Exercises 1.4, Problem 6).