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 0.1, (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. 10. y' = y(3-ty), y(0) = 0.5

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 0.1, (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. 10. y' = y(3-ty), y(0) = 0.5

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

10a

7) ly - C ng ng 8) is ne or er ny nd es, ne a st SO on of que on ch y' = 3+t-y, y' = 2y = 1, y' = 0.5-1 + 2y, y(0) = 1 4. y' = 3 cost - 2y, y(0) = 0 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 converging or diverging. G 5. y'=5-3√√y 6. y' = y(3- ty) 7. y' = -ty+0.1y³ 8. y' = 1² + y² 1. 2. 3. G y(0) = 1 y(0) = 1 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 11. Consider the initial value problem y' = 31² 3y² - 4' es y(1) = 0. Na. Use Euler's method with h = 0.1 to obtain approximate values of the solution at t = 1.2, 1.4, 1.6, and 1.8. Nb. 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 15 c AU = 1.8. Also note (from the differential equation) that for t the line tangent to the solution is parallel to the y-axis when y = ±2/√√3 = ±1.155. Explain how this might cause such a difference in the calculated values. N 12. Consider the initial value problem y' = 1² + y², y(0) = 1. where a is a given number. value ao. Nb. Use Eul by restricting 14. Consider the where a is a giver Ga. Draw that there is that separate critical value N b. Use E by restrictin Convergen 15. under suitable generated by t y' = f(t, y), y size h decreases. the initial value Use Euler's method with h = 0.1, 0.05, 0.025, and 0.01 to explore the solution of this problem for 0 ≤ t ≤ 1. What is your best estimate 0.8? At t = 1? Are your results of the value of the solution at t = 0.8? At t consistent with the direction field in Problem 8? 13. Consider the initial value problem y = -ty+0.1y³, y(0) = a, a. Show N b. Usi Yk c. Notin that for each d. Con: h = (t as n → nx Hint: I n In each of Pr 15 to show converges to 16. y' = 17. y' =
Transcribed Image Text:7) ly - C ng ng 8) is ne or er ny nd es, ne a st SO on of que on ch y' = 3+t-y, y' = 2y = 1, y' = 0.5-1 + 2y, y(0) = 1 4. y' = 3 cost - 2y, y(0) = 0 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 converging or diverging. G 5. y'=5-3√√y 6. y' = y(3- ty) 7. y' = -ty+0.1y³ 8. y' = 1² + y² 1. 2. 3. G y(0) = 1 y(0) = 1 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 11. Consider the initial value problem y' = 31² 3y² - 4' es y(1) = 0. Na. Use Euler's method with h = 0.1 to obtain approximate values of the solution at t = 1.2, 1.4, 1.6, and 1.8. Nb. 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 15 c AU = 1.8. Also note (from the differential equation) that for t the line tangent to the solution is parallel to the y-axis when y = ±2/√√3 = ±1.155. Explain how this might cause such a difference in the calculated values. N 12. Consider the initial value problem y' = 1² + y², y(0) = 1. where a is a given number. value ao. Nb. Use Eul by restricting 14. Consider the where a is a giver Ga. Draw that there is that separate critical value N b. Use E by restrictin Convergen 15. under suitable generated by t y' = f(t, y), y size h decreases. the initial value Use Euler's method with h = 0.1, 0.05, 0.025, and 0.01 to explore the solution of this problem for 0 ≤ t ≤ 1. What is your best estimate 0.8? At t = 1? Are your results of the value of the solution at t = 0.8? At t consistent with the direction field in Problem 8? 13. Consider the initial value problem y = -ty+0.1y³, y(0) = a, a. Show N b. Usi Yk c. Notin that for each d. Con: h = (t as n → nx Hint: I n In each of Pr 15 to show converges to 16. y' = 17. y' =
Expert Solution
trending now

Trending now

This is a popular 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