Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
3. Use method of undetermined coefficients 2X y" - 4y = 8xe

3. Use method of undetermined coefficients 2X y" - 4y = 8xe

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

Can you solve this equation using the given flow for the method of undetermined coefficients?

3. Use method of undetermined coefficients

y'' - 4y = 8xe2x

Example 2 Find the general solution : y" + 2y' + y = 7 + 75 sin 2x Solution: Thus, m² + 2m + 1 = 0 Yp = = = (m+1) (m+1) = 0 Yc = C₁ ex + C₂ xe-x R(x) = 7+75 sin 2x A + B cos 2x + C sin 2x Yp -2B sin 2x + 2C cos 2x Yp" = -4B cos2x · 4C sin 2x suggests roots of 0 and +2i - 4B cos 2x -4Csin 2x + 2(-2B sin 2x + 2C cos 2x) + A + B cos 2x + C sin 2x = 7+75 sin 2x Equating coefficients : Solving simultaneously for constant : A = 7 Cos 2x - 4B + 4C + B = 0 Sin 2x : -4C-4B + C = 75 4C3B = 0 -3C-4B = 75 B = -12 and C= -9 yp = 7-12 cos 2x - 9 sin 2x The general solution is y=ex (C₁ + C₂ x) + 7-12 cos 2x - 9 sin 2x
Transcribed Image Text:Example 2 Find the general solution : y" + 2y' + y = 7 + 75 sin 2x Solution: Thus, m² + 2m + 1 = 0 Yp = = = (m+1) (m+1) = 0 Yc = C₁ ex + C₂ xe-x R(x) = 7+75 sin 2x A + B cos 2x + C sin 2x Yp -2B sin 2x + 2C cos 2x Yp" = -4B cos2x · 4C sin 2x suggests roots of 0 and +2i - 4B cos 2x -4Csin 2x + 2(-2B sin 2x + 2C cos 2x) + A + B cos 2x + C sin 2x = 7+75 sin 2x Equating coefficients : Solving simultaneously for constant : A = 7 Cos 2x - 4B + 4C + B = 0 Sin 2x : -4C-4B + C = 75 4C3B = 0 -3C-4B = 75 B = -12 and C= -9 yp = 7-12 cos 2x - 9 sin 2x The general solution is y=ex (C₁ + C₂ x) + 7-12 cos 2x - 9 sin 2x
3. Use method of undetermined coefficients 2X y" - 4y = 8xe
Transcribed Image Text:3. Use method of undetermined coefficients 2X y" - 4y = 8xe
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

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