In this problem you will solve the nonhomogeneous system -2e¹ = [_$__3] + [-²] 4 21 ÿ -9 A. Write a fundamental matrix for the associated homogeneous system Y = Y-1 = B. Compute the inverse -1 Y ģ dt 15 ÿ' e^(t)(-cos(3t)+sin(3t)) = + 3e^(t)cos(3t) C. Multiply by g and integrate e^(-t) sin(3t) -e^(-t)cos(3t) (Do not include c₁ and c₂ in your answers). D. Give the solution to the system e^(t)(-cos(3t)+sin(3t)) 2/3cos(3t)-2357/15000cos(3t+pi/4) 2/3sin(3t)-2357/15000sin(3t+pi/4) 3e^(t)cos(3t) e^(t)(-cos(3t)-sin(3t)) 3e^(t)sin(3t) (Do not include c₁ and c₂ in your answers). |] 0.471e^(-t)sin(3t+pi/4) -0.471e^(-t)cos(3t+pi/4) 2/3cos(3t)-2357/15000cos(3t+pi/4) 2/3sin(3t)-2357/15000sin(3t+pi/4) C₁+ +91 +C₂ e^(t)(-cos(3t)-sin(3t)) 3e^(t) sin(3t) C2
In this problem you will solve the nonhomogeneous system -2e¹ = [_$__3] + [-²] 4 21 ÿ -9 A. Write a fundamental matrix for the associated homogeneous system Y = Y-1 = B. Compute the inverse -1 Y ģ dt 15 ÿ' e^(t)(-cos(3t)+sin(3t)) = + 3e^(t)cos(3t) C. Multiply by g and integrate e^(-t) sin(3t) -e^(-t)cos(3t) (Do not include c₁ and c₂ in your answers). D. Give the solution to the system e^(t)(-cos(3t)+sin(3t)) 2/3cos(3t)-2357/15000cos(3t+pi/4) 2/3sin(3t)-2357/15000sin(3t+pi/4) 3e^(t)cos(3t) e^(t)(-cos(3t)-sin(3t)) 3e^(t)sin(3t) (Do not include c₁ and c₂ in your answers). |] 0.471e^(-t)sin(3t+pi/4) -0.471e^(-t)cos(3t+pi/4) 2/3cos(3t)-2357/15000cos(3t+pi/4) 2/3sin(3t)-2357/15000sin(3t+pi/4) C₁+ +91 +C₂ e^(t)(-cos(3t)-sin(3t)) 3e^(t) sin(3t) C2
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
Calculate to the answers for questions below:
D. Give the solution to the system:
ASAP
![In this problem you will solve the nonhomogeneous system
-2e¹
= [_$__3] + [-²]
4 21
ÿ
-9
A. Write a fundamental matrix for the associated homogeneous system
Y =
Y-1 =
B. Compute the inverse
-1
Y ģ dt
15
ÿ'
e^(t)(-cos(3t)+sin(3t))
=
+
3e^(t)cos(3t)
C. Multiply by g and integrate
e^(-t) sin(3t)
-e^(-t)cos(3t)
(Do not include c₁ and c₂ in your answers).
D. Give the solution to the system
e^(t)(-cos(3t)+sin(3t))
2/3cos(3t)-2357/15000cos(3t+pi/4)
2/3sin(3t)-2357/15000sin(3t+pi/4)
3e^(t)cos(3t)
e^(t)(-cos(3t)-sin(3t))
3e^(t)sin(3t)
(Do not include c₁ and c₂ in your answers).
|]
0.471e^(-t)sin(3t+pi/4)
-0.471e^(-t)cos(3t+pi/4)
2/3cos(3t)-2357/15000cos(3t+pi/4)
2/3sin(3t)-2357/15000sin(3t+pi/4)
C₁+
+91
+C₂
e^(t)(-cos(3t)-sin(3t))
3e^(t) sin(3t)
C2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F89dc5364-eb63-4681-92b5-ce2b0a52188e%2F756daa03-93c7-4ab3-b709-b91ad4a3179e%2Fs4kwl1v_processed.png&w=3840&q=75)
Transcribed Image Text:In this problem you will solve the nonhomogeneous system
-2e¹
= [_$__3] + [-²]
4 21
ÿ
-9
A. Write a fundamental matrix for the associated homogeneous system
Y =
Y-1 =
B. Compute the inverse
-1
Y ģ dt
15
ÿ'
e^(t)(-cos(3t)+sin(3t))
=
+
3e^(t)cos(3t)
C. Multiply by g and integrate
e^(-t) sin(3t)
-e^(-t)cos(3t)
(Do not include c₁ and c₂ in your answers).
D. Give the solution to the system
e^(t)(-cos(3t)+sin(3t))
2/3cos(3t)-2357/15000cos(3t+pi/4)
2/3sin(3t)-2357/15000sin(3t+pi/4)
3e^(t)cos(3t)
e^(t)(-cos(3t)-sin(3t))
3e^(t)sin(3t)
(Do not include c₁ and c₂ in your answers).
|]
0.471e^(-t)sin(3t+pi/4)
-0.471e^(-t)cos(3t+pi/4)
2/3cos(3t)-2357/15000cos(3t+pi/4)
2/3sin(3t)-2357/15000sin(3t+pi/4)
C₁+
+91
+C₂
e^(t)(-cos(3t)-sin(3t))
3e^(t) sin(3t)
C2
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