Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Consider the second-order system of differential equations dx dt² 11x + 8y, d'y dt² =8x-y. 11 8 The coefficient matrix has eigenvectors [2] an [1] and [2¹] and the corresponding 8 eigenvalues are 15 and -5. Select the option that gives the general solution of this system. Select one: evst + Ca [2¹]. [3] = [*] = ₁ [i] cos(√/15t) + C₂ [1] sin(√/15t) + C₁ [2¹] [2¹] coa( √/15t) + C₂ [2] sin(√15t) + O₂ [₁] cos(√15t) + C₂ [1] si [²] %[1]. ¹ + 0₂ [²] • e vot = C₁ sin(√15t) + C₂ [2²¹] cos(√5t) + 0₂ [2¹] sin(√5t) [i] = ª[i]²+₂ [i]<√²+₁ [1¹] ca[(√St) + C [1] (VB) e -Vist C3 si sin(√5t) O O O O N evse

Consider the second-order system of differential equations dx dt² 11x + 8y, d'y dt² =8x-y. 11 8 The coefficient matrix has eigenvectors [2] an [1] and [2¹] and the corresponding 8 eigenvalues are 15 and -5. Select the option that gives the general solution of this system. Select one: evst + Ca [2¹]. [3] = [*] = ₁ [i] cos(√/15t) + C₂ [1] sin(√/15t) + C₁ [2¹] [2¹] coa( √/15t) + C₂ [2] sin(√15t) + O₂ [₁] cos(√15t) + C₂ [1] si [²] %[1]. ¹ + 0₂ [²] • e vot = C₁ sin(√15t) + C₂ [2²¹] cos(√5t) + 0₂ [2¹] sin(√5t) [i] = ª[i]²+₂ [i]<√²+₁ [1¹] ca[(√St) + C [1] (VB) e -Vist C3 si sin(√5t) O O O O N evse

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

q11

Consider the second-order system of differential equations d'a = 11x + 8y, d'y dt² = 8x-y. dt² 11 8 The coefficient matrix has eigenvectors and 8 -1 eigenvalues are 15 and -5. Select the option that gives the general solution of this system. Select one: O [] = a[i] cos(√15t) + C₂ [1]. sin (√15t) + C3 cos(√15t) + C₂ [2¹] sin(√15t) +0₁ []=[2 C₁ [3] = a₁ [i] cos(√15t) + C₂ [2] si sin(√15t) + C3 []=[]+[i]+[2¹] 008(√58) + C₂ [¹] ² (√56) C₁ evist C₂ e C3 CA sin O O O [2] and the corresponding 3 [2²] evst + 4 [2¹] + C₂ • [1] - e-vot • [2] evst - [2²] cos(√5t) + C4 [2¹] sin(√5t) +0₂ e-vst
Transcribed Image Text:Consider the second-order system of differential equations d'a = 11x + 8y, d'y dt² = 8x-y. dt² 11 8 The coefficient matrix has eigenvectors and 8 -1 eigenvalues are 15 and -5. Select the option that gives the general solution of this system. Select one: O [] = a[i] cos(√15t) + C₂ [1]. sin (√15t) + C3 cos(√15t) + C₂ [2¹] sin(√15t) +0₁ []=[2 C₁ [3] = a₁ [i] cos(√15t) + C₂ [2] si sin(√15t) + C3 []=[]+[i]+[2¹] 008(√58) + C₂ [¹] ² (√56) C₁ evist C₂ e C3 CA sin O O O [2] and the corresponding 3 [2²] evst + 4 [2¹] + C₂ • [1] - e-vot • [2] evst - [2²] cos(√5t) + C4 [2¹] sin(√5t) +0₂ e-vst
Expert Solution
steps

Step by step

Solved in 2 steps with 1 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