Solution: Use the Modified Euler method to approximate the solutions to each of the

Chapter 5, Problem 3

(choose chapter or problem)

Use the Modified Euler method to approximate the solutions to each of the following initial-value problems and compare the results to the actual values. a. y'= y/t (y/t)2 , 1 < r < 2, y(l) = 1, with/i = 0.1; actual solution y(r) = r/(l +In r). b. y' = l+y/r+fy/r)2 , 1 < r < 3, y(l) = 0, with/? = 0.2; actual solutiony(r) = rtan{lnr). c. y' = (y + l)(y + 3), 0 < r < 2, y(0) = -2, with h 0.2; actual solution y(r) - -3 + 2(1 + e~2 ')~l . d. y'=-5y+5r2 +2r, 0 < r < 1, y(0) = y, with/? = 0.1; actual solution y(r) = r 2 + jc_5'.