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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F275d4d30-8cac-408b-9dfa-7a6bd0ed4b12%2F2bd58fd5-5d58-4bd0-bb1b-ee510bef9976%2Fq9cjvz5_processed.png&w=3840&q=75)
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
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