Calculator Again Consider the IVP y' = ty, y(0) = 1.(a) Use Euler’s method to approxim...

Calculator Again Consider the IVP y' = ty, y(0) = 1.

(a) Use Euler’s method to approximate the solution at t = 1 with step sizes 1, 1/2, 1/4, and 1/8.

(b) Solve the problem exactly, and compare the result at t = 1 with the approximations calculated in part (a).

Computer Help Advisable Use of a programmable calculator or computer is advisable for carrying out numerical approximations. A spreadsheet is especially effective in many cases. Euler’s method formulas for solving the IVP y' = t − y, y(0) = 1 on [0, 2] with step size 0.2 are illustrated here.

NOTE: The formulas in line 3 are from equations (5) and (6). Lines 4–12 need not be typed separately; they just repeat the instructions given on line 3, with spreadsheet shortcuts. See Appendix SS for details.