Consider the second-order system of differential equations d²x dt² d'y dt2 =x+3y, The coefficient matrix are 4 and -2. 1 3 31 3x + y. has eigenvectors Hand [¹] ADDEN WEWMAND and the corresponding eigenvalues wwwwwwwww
Consider the second-order system of differential equations d²x dt² d'y dt2 =x+3y, The coefficient matrix are 4 and -2. 1 3 31 3x + y. has eigenvectors Hand [¹] ADDEN WEWMAND and the corresponding eigenvalues wwwwwwwww
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![Consider the second-order system of differential equations
d²x
dt²
d²y
dt2
=x+3y,
The coefficient matrix
1 3
3
3x+y.
wwwwww
has eigenvectors
Hand [1]
are 4 and - 2.
Select the option that gives the general solution of this system.
Select one:
° 1) = 0[¹] con (24) + C₁ [₁] (²0₁₁+₂
[1¹]
CA
cos(2t)
sin(2t) + C3 ev2t
[*] = C₁ [1] cos(2t) + 0₂
sin(2t) + C3
cos(√2t) + C4
Casin(√21)
= +
HHH] co √21) + C [¹] sin (√2)
C₁ e2t
cos(√2t) C4
C3
and the corresponding eigenvalues
[3] = C₁ [1] cos(2t) + C₂
e2t
2t
[1] = ₂ [1] ² + ₂ [1] ² ² + ₁ [₁¹] e√²+ + C₁ [ 1¹ ] e-√₂²
2t
e
C4
A WEW MEXAND
sin(2t) + C3
· [₁¹] ₁ √²+ + 0₁ [1¹] ₁ = √²
√√2t
e](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F413a57ab-c507-4b37-84c4-d6f24b4c88c2%2Fd7e476d1-8530-4bd2-b429-a75b487b0e18%2Ftormrbn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the second-order system of differential equations
d²x
dt²
d²y
dt2
=x+3y,
The coefficient matrix
1 3
3
3x+y.
wwwwww
has eigenvectors
Hand [1]
are 4 and - 2.
Select the option that gives the general solution of this system.
Select one:
° 1) = 0[¹] con (24) + C₁ [₁] (²0₁₁+₂
[1¹]
CA
cos(2t)
sin(2t) + C3 ev2t
[*] = C₁ [1] cos(2t) + 0₂
sin(2t) + C3
cos(√2t) + C4
Casin(√21)
= +
HHH] co √21) + C [¹] sin (√2)
C₁ e2t
cos(√2t) C4
C3
and the corresponding eigenvalues
[3] = C₁ [1] cos(2t) + C₂
e2t
2t
[1] = ₂ [1] ² + ₂ [1] ² ² + ₁ [₁¹] e√²+ + C₁ [ 1¹ ] e-√₂²
2t
e
C4
A WEW MEXAND
sin(2t) + C3
· [₁¹] ₁ √²+ + 0₁ [1¹] ₁ = √²
√√2t
e
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