Hello, I am having a hard time finding x(t) and y(t), highlighted in yellow. I have a feeling it has to do with how I am finding the c1 and c2 constants based upon applying Euler's formula for complex eigenvalues and eigenvectors. Could you please check and if it is not right, please explain the steps clearly to resolve? Appreciate your help, thank you! 22 XMEAN-37-12 Y2₁ = -5 +5;(A-AI) V = 02-(-5+51) 2-377+51تےQ75-2 1712-(-541)2t(7+51) V₁ + 2√₂ = 0I[UE]V₂X (0) = 4; y (0) = 192₂ = -5-51X₁ (t) = p (²5+51)+7+51)e.-It (cost + i sint) (-217+51V/₁V/₂อ-2開 [:]+ G₂2₂7T07550275-0120-21055([7. 105 56 - 5 sinf7] + Giet [ - 2 sin 5tstL7 cossz +5 sin st0[23/1 = = ²⇒-2C₁ = 4G=-2-76₁+ C₂ = -197(-2) + (₂=-195=23_x²+) = (-2X-2) €²²7 (05 5+ + (-5)(-₂) esinst-57,= че-я cosst +10 e-sin 5ty (t) = (-2) (7) € ²³ 405 47-50-2²sin 57 +57 (7) 6²40557+ bestsinst= 14 escos St +35 et os st+ De-st sin st

Introduction: Euler's formula for the complex numbers is given as: ei θ = cos(θ) + i sin(θ) Given:…

Answered: 22 ]]] 十 x(0) = 4; y(0)= 19

Math

Advanced Math

22 ]]] 十 x(0) = 4; y(0)= 19

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

Hello, I am having a hard time finding x(t) and y(t), highlighted in yellow. I have a feeling it has to do with how I am finding the c₁ and c₂ constants based upon applying Euler's formula for complex eigenvalues and eigenvectors. Could you please check and if it is not right, please explain the steps clearly to resolve? Appreciate your help, thank you!

22 X
MEAN
-37-12 Y
2₁ = -5 +5;
(A-AI) V = 0
2-(-5+51) 2
-37
7+51
تے
Q
75-2 17
12-(-541)
2
t
(7+51) V₁ + 2√₂ = 0
I[UE]
V₂
X (0) = 4; y (0) = 19
2₂ = -5-51
X₁ (t) = p (²5+51)+
7+51)
e
.-It (cost + i sint) (-2
17+51
V/₁
V/₂
อ
-2
開 [:]
+ G₂2₂
7
T
0
7550275-012
0
-21055
([7. 105 56 - 5 sinf7] + Giet [ - 2 sin 5t
st
L7 cossz +5 sin st
0
[23/1 = = ²
⇒-2C₁ = 4
G=-2
-76₁+ C₂ = -19
7(-2) + (₂=-19
5=23
_x²+) = (-2X-2) €²²7 (05 5+ + (-5)(-₂) esinst
-57,
= че-я cosst +10 e-sin 5t
y (t) = (-2) (7) € ²³ 405 47-50-2²sin 57 +57 (7) 6²40557
+ bestsinst
= 14 escos St +35 et os st
+ De-st sin st

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