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 Euler’s method (4) with h = 0.1 to approximate the solution to the initial value problem

on the interval (that is, at x = 0, 0.1, . . . , 1.0). Compare your answers with the actual solution y = e^-20xWhat went wrong? Next, try the step size h = 0.025 and also h = 0.2. What conclusions can you draw concerning the choice of step size?