Note: The application following this problem set lists illustrative calculator/computer pr...

Note: The application following this problem set lists illustrative calculator/computer programs that can be used in Problems through.

A programmable calculator or a computer will be useful for Problems through. In each problem find the exact so-lution of the given initial value problem. Then apply the improved Euler method twice to approximate (to five decimal places) this solution on the given interval, first with step size h = 0.01, then with step size h = 0.005. Make a table showing the approximate values and the actual value, together with the percentage error in the more accurate approximations, for x an integral multiple (if 0.2. Throughout, primes denote derivatives with respect to x.