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

Chapter 5, Problem 1

(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' = re3 ' ly, 0 < r < 1, ,y(0) = 0, with h = 0.5; actual solution y(t) = ire3 ' ^e3 ' + -Lg-2' 25 b. /= 1 + (r y)2 , 2 < r < 3, >>(2) = I, with h = 0.5; actual solution v(r) = t + c. y' = \+ylt, 1 < r < 2, >'(1) = 2, with/?= 0.25; actual solution ylr) = r In r + 2r. d. y' cos2r + sin3r, 0 < r < 1, v(0) 1, with h 0.25; actual solution >'(r) \ sin 2r y cos 3r + |.