Question

January 19, 2018 This homeworksheet is due in class on Wednesday, January 24. The problems are similar to problems from your textbook Question: 23 Points: Score: 4 4 24 16 oximate the solution to the given 1. (16 points) Use Euler's Method with the given step size Ar to appr initial value problem. Your answer should have a table with approximate outputs at each step. (a) 2)0 + 7), y(O) 3.5, Ar 0.5. Approximate y(3). (b) dy =-3y + 1, y(0) = 4, Δ, = 0.25. Approximate y(1) (c) 3--3y + 1, y(3)-4, Δ1-0.25. Approximate y(4). (d) = y2-1, y(0) 1, Δ 0.25. Approximate y( 1) 2. (4 points) Sketch a slope field for the differential equation in part (a) above, along with the solution t the given initial value pro values given by Euler's Method blem using the slope field. Comment on how this differs from the approximate ation about the answers to parts (b) and (c) in 3. (4 points) Use a slope field to explain the obvious observ question1

need help with #2 & #3

Answer 1

Solution;-

Euter method y_n + 1 = y_n + n f (t_n, y_n) dy/dt = - (y -2) (y + 7), y (0) = 0.5 To find y (3) y_n + 1 = y_n + h f (t_n, y_n) y (0.5) = y (0) + 0 5 f (0, 3.5) y(0.5) = 3.5 + 0.5 [- (3.5 -2) (3.5 + 7)] y (0.5) = 3.5 -7.875 y (0.5) = -4.375 y (1) = -4.375 + 0.5 [- (- 4.375 -2) (- 4.375 + 7)] y (1) = 4.375 + 803671875 y (1) = 3.9921875 y (1.5) = 3.9921875 + 0.5[- (9921875 -2) (3.9921875 + 7)] y (1.5) = -6.957061768 y (1.5) = 6.9757061768 y (2) = -6.9757061768 + 0.5 [- (- 6.9757061768 -2) (- 6.9757061768 -7_] y (2) = -6.7830056998 y (2.5) = -6.783 + 0.5 [- (- 6.783 -2)