We have found the following particular solution and its derivatives. Yp = Ax² + Bx + C + (Dx + E)e* Yp = 2AX + B + (Dx + E)e* + Dex = 2A + (Dx + E)e* + 2De* "1 Ур Substituting into the original differential equation results in the following. y" - 8y' + 20y = 200x² - 52xe* (2A + (Dx + E)e* + 2Dex) - 8(2Ax + B+ (Dx + E)ex + Dex) + 20(Ax2 + Bx + C+ (Dx + E)ex) = 200x² - 52xe*' Simplifying the left side of this equation gives the following. (2A+ (Dx + E)ex + 2Dex) - 8(2Ax+ B + (Dx + E)ex + De*) + 20(Ax² + Bx + C + (Dx + E)e*) = (2A - 8B + 20C) + (-16A + 20B)x+ (-6D+ 13E)e* + ²+( 13 ✓ )oxe* + (20 4x² As the coefficients of the terms in this simplified expression must be equal to the coefficients of 200x² - 52xe, we have the following system. 2A8B+20C = 0 -16A + 20B = -6D + 13E=0 x )D x 4 = 200 = -52
We have found the following particular solution and its derivatives. Yp = Ax² + Bx + C + (Dx + E)e* Yp = 2AX + B + (Dx + E)e* + Dex = 2A + (Dx + E)e* + 2De* "1 Ур Substituting into the original differential equation results in the following. y" - 8y' + 20y = 200x² - 52xe* (2A + (Dx + E)e* + 2Dex) - 8(2Ax + B+ (Dx + E)ex + Dex) + 20(Ax2 + Bx + C+ (Dx + E)ex) = 200x² - 52xe*' Simplifying the left side of this equation gives the following. (2A+ (Dx + E)ex + 2Dex) - 8(2Ax+ B + (Dx + E)ex + De*) + 20(Ax² + Bx + C + (Dx + E)e*) = (2A - 8B + 20C) + (-16A + 20B)x+ (-6D+ 13E)e* + ²+( 13 ✓ )oxe* + (20 4x² As the coefficients of the terms in this simplified expression must be equal to the coefficients of 200x² - 52xe, we have the following system. 2A8B+20C = 0 -16A + 20B = -6D + 13E=0 x )D x 4 = 200 = -52
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
The bottom two questions are wrong (A&D). A can't be 10, that is wrong. D can't be -4, that is wrong as well.
Transcribed Image Text:Step 4
We have found the following particular solution and its derivatives.
Yp = Ax² + Bx + C + (Dx + E)e*
= 2AX + B + (Dx + E)ex + Dex
= 2A + (Dx + E)ex + 2De*
Substituting into the original differential equation results in the following.
y" - 8y' + 20y = 200x² - 52xe*
ур
4
YP
(2A + (Dx + E)e* + 2Dex) - 8(2Ax + B + (Dx + E)ex + Dex) + 20(Ax² + Bx + C + (Dx + E)ex) = 200x² - 52xe*
Simplifying the left side of this equation gives the following.
5
(2A+ (Dx + E)ex + 2De*) - 8(2Ax + B + (Dx + E)ex + Dex)
+ 20(Ax² + Bx + C + (Dx + E)e*)
= (2A – 8B + 20C) + (−16A + 20B)x + (−6D + 13E)e* +(13
✓ )oxe* + (20
JAx²
As the coefficients of the terms in this simplified expression must be equal to the coefficients of 200x² - 52xe, we have the following system.
2A - 8B + 20C = 0
-16A + 20B = 0
-6D + 13E = 0
) D =
* A = 200
IL
X
-52
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 6 steps with 6 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
