Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
In each of Problems 9 and 10, use Euler's method to find approximate values of the solution of the given initial value problem at t = 0.5, 1, 1.5, 2, 2.5, and 3: (a) With h = 0.1, (b) With h = 0.05, (c) With h = 0.025, (d) With h = 0.01. N 9. y'= 5-3√√y, y(0) = 2

In each of Problems 9 and 10, use Euler's method to find approximate values of the solution of the given initial value problem at t = 0.5, 1, 1.5, 2, 2.5, and 3: (a) With h = 0.1, (b) With h = 0.05, (c) With h = 0.025, (d) With h = 0.01. N 9. y'= 5-3√√y, y(0) = 2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

9a 

 

converging or diverging. In each of Problems 5 through 8, draw a direction field for the given differential equation and state whether you think that the solutions are 5. y' = 5-3√y y' = y(3-ty) G G G 6 6. 7. 8. y'= -ty+0.1y³ y' = 1² + y² G In each of Problems 9 and 10, use Euler's method to find approximate values of the solution of the given initial value problem at t = 0.5, 1, 1.5, 2, 2.5, and 3: (a) With h = 0.1, (b) With h = 0.05, (c) With h = 0.025, (d) With h = 0.01. N 9. y' = 5-3√√y, y(0) = 2 N 10. y'= y(3-ty), y(0) = 0.5 Consider the initial value problem 11. y' = 3t² 3y² - 4' y(1) = 0. when y' = 1² + y², y(0) = 1. (1) 15. un ge y' si: th Na. Use Euler's method with h = 0.1 to obtain approximate o values of the solution at t = 1.2, 1.4, 1.6, and 1.8. N b. Repeat part a with h = 0.05. c. Compare the results of parts a and b. Note that they are reasonably close for t = 1.2, 1.4, and 1.6 but are quite different for t = 1.8. Also note (from the differential equation) that the line tangent to the solution is parallel to the y-axis when +2/√3 ±1.155. Explain how this might cause such y a difference in the calculated values. N 12. Consider the initial value problem Use Euler's method with h = 0.1, 0.05, 0.025, and 0.01 to explore the What is your best estimate solution of this problem
Transcribed Image Text:converging or diverging. In each of Problems 5 through 8, draw a direction field for the given differential equation and state whether you think that the solutions are 5. y' = 5-3√y y' = y(3-ty) G G G 6 6. 7. 8. y'= -ty+0.1y³ y' = 1² + y² G In each of Problems 9 and 10, use Euler's method to find approximate values of the solution of the given initial value problem at t = 0.5, 1, 1.5, 2, 2.5, and 3: (a) With h = 0.1, (b) With h = 0.05, (c) With h = 0.025, (d) With h = 0.01. N 9. y' = 5-3√√y, y(0) = 2 N 10. y'= y(3-ty), y(0) = 0.5 Consider the initial value problem 11. y' = 3t² 3y² - 4' y(1) = 0. when y' = 1² + y², y(0) = 1. (1) 15. un ge y' si: th Na. Use Euler's method with h = 0.1 to obtain approximate o values of the solution at t = 1.2, 1.4, 1.6, and 1.8. N b. Repeat part a with h = 0.05. c. Compare the results of parts a and b. Note that they are reasonably close for t = 1.2, 1.4, and 1.6 but are quite different for t = 1.8. Also note (from the differential equation) that the line tangent to the solution is parallel to the y-axis when +2/√3 ±1.155. Explain how this might cause such y a difference in the calculated values. N 12. Consider the initial value problem Use Euler's method with h = 0.1, 0.05, 0.025, and 0.01 to explore the What is your best estimate solution of this problem
S 9. a. 2.30800, 2.49006, 2.60023, 2.66773, 2.70939, 2.73521 10. a. b. 2.30167, 2.48263, 2.59352, 2.66227, 2.70519, 2.73209 c. 2.29864, 2.47903, 2.59024, 2.65958, 2.70310, 2.73053 d. 2.29686, 2.47691, 2.58830, 2.65798, 2.70185, 2.72959 1.70308, 3.06605, 2.44030, 1.77204, 1.37348, 1.11925 1.79548, 3.06051, 2.43292, 1.77807, 1.37795, 1.12191 c. 1.84579, 3.05769, 2.42905, 1.78074, 1.38017, 1.12328 d. 1.87734, 3.05607, 2.42672, 1.78224, 1.38150, 1.12411 b. 11. a. -0.166134, -0.410872, -0.804660, 4.15867 b. -0.174652, -0.434238, -0.889140, -3.09810 12. A reasonable estimate for y at t = 0.8 is between 5.5 and 6. No reliable estimate is possible at t = 1 from the specified data. 13. b. 2.37 < a < 2.38 < 0.68 14. b. 0.67 < a % Section 2.8, page 90 dw/ds = (s + 1)² + (w+2)2, w(0) = 0 dw/ds = 1-(w+3)³, w(0) = 0 n 2k tk 3. a. ,(t) = Σ k! k=1 (t) = e²t - 1 1. 2. c. lim 848 4. a. (1) = n k=1 c. lim (t) = 4e-1/2 +21-4 88 ¡2k-1 n 5. a. Φ„(1) = Σ k=1 (-1)k+1 pk+1 /(k + 1)!2k-1 11 1 n 1.3.5 (2k-1) t3k-1 5.8 (3k-1) · m T
Transcribed Image Text:S 9. a. 2.30800, 2.49006, 2.60023, 2.66773, 2.70939, 2.73521 10. a. b. 2.30167, 2.48263, 2.59352, 2.66227, 2.70519, 2.73209 c. 2.29864, 2.47903, 2.59024, 2.65958, 2.70310, 2.73053 d. 2.29686, 2.47691, 2.58830, 2.65798, 2.70185, 2.72959 1.70308, 3.06605, 2.44030, 1.77204, 1.37348, 1.11925 1.79548, 3.06051, 2.43292, 1.77807, 1.37795, 1.12191 c. 1.84579, 3.05769, 2.42905, 1.78074, 1.38017, 1.12328 d. 1.87734, 3.05607, 2.42672, 1.78224, 1.38150, 1.12411 b. 11. a. -0.166134, -0.410872, -0.804660, 4.15867 b. -0.174652, -0.434238, -0.889140, -3.09810 12. A reasonable estimate for y at t = 0.8 is between 5.5 and 6. No reliable estimate is possible at t = 1 from the specified data. 13. b. 2.37 < a < 2.38 < 0.68 14. b. 0.67 < a % Section 2.8, page 90 dw/ds = (s + 1)² + (w+2)2, w(0) = 0 dw/ds = 1-(w+3)³, w(0) = 0 n 2k tk 3. a. ,(t) = Σ k! k=1 (t) = e²t - 1 1. 2. c. lim 848 4. a. (1) = n k=1 c. lim (t) = 4e-1/2 +21-4 88 ¡2k-1 n 5. a. Φ„(1) = Σ k=1 (-1)k+1 pk+1 /(k + 1)!2k-1 11 1 n 1.3.5 (2k-1) t3k-1 5.8 (3k-1) · m T
Expert Solution
steps

Step by step

Solved in 8 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS