Consider the ODE With the initial condition that y=1 when x = 1. Show that the particular solution is y=(lnx² + x³ +2). b. Use the 2nd, 3rd and 4 Runge-Kutta methods to approximate the value of y at x = 2 using a step size of h = 0.1. Complete the table below. RK Method Step size Approx. value of y Abs. Err. Rel. Abs. Err. (%) RK-2 a. RK-5 RK-4 0.1 0.1 y² + ²y = 23 +1 0.1 Show sample of computation below (and attach soft copy of Excel computation).
Consider the ODE With the initial condition that y=1 when x = 1. Show that the particular solution is y=(lnx² + x³ +2). b. Use the 2nd, 3rd and 4 Runge-Kutta methods to approximate the value of y at x = 2 using a step size of h = 0.1. Complete the table below. RK Method Step size Approx. value of y Abs. Err. Rel. Abs. Err. (%) RK-2 a. RK-5 RK-4 0.1 0.1 y² + ²y = 23 +1 0.1 Show sample of computation below (and attach soft copy of Excel computation).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please make sure the answer is correct. thank you
![1.
Consider the ODE
With the initial condition that y=1 when x = 1.
LA3.3
Numerical Methods for Solving ODE
Runge-Kutta Method
a. Show that the particular solution is y=- (In x² + x³ + 2).
1
3x-2
RK-2
b. Use the 2nd, 3rd and 4th Runge-Kutta methods to approximate the value of y at x = 2 using a step
size of h = 0.1. Complete the table below.
RK-3
RK Method Step size Approx. value of y Abs. Err. Rel. Abs. Err. (%)
RK-4
2
y² + ²y = 3³+
y'
0.1
+1
0.1
0.1
Show sample of computation below (and attach soft copy of Excel computation).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff585c19b-ef83-4b9a-93dd-0cb9fc8d5f5b%2Fcfe25d43-6c90-4a1c-8fc1-27646e673cd9%2Fir4zhym_processed.png&w=3840&q=75)
Transcribed Image Text:1.
Consider the ODE
With the initial condition that y=1 when x = 1.
LA3.3
Numerical Methods for Solving ODE
Runge-Kutta Method
a. Show that the particular solution is y=- (In x² + x³ + 2).
1
3x-2
RK-2
b. Use the 2nd, 3rd and 4th Runge-Kutta methods to approximate the value of y at x = 2 using a step
size of h = 0.1. Complete the table below.
RK-3
RK Method Step size Approx. value of y Abs. Err. Rel. Abs. Err. (%)
RK-4
2
y² + ²y = 3³+
y'
0.1
+1
0.1
0.1
Show sample of computation below (and attach soft copy of Excel computation).
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 8 steps with 10 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)