Find the general solution of the system X'(t) = AX(t) for the given matrix A. A = © = O Oxt) = creP[3] + cze[3] ©xt) = cre 24 25 ၁ =ix) ,io+ ]၃၀-၁ []၁၁ ]၉၀+၁ = (၂) ၀၁ + F]galow ux ၁ + [၃]၁
Find the general solution of the system X'(t) = AX(t) for the given matrix A. A = © = O Oxt) = creP[3] + cze[3] ©xt) = cre 24 25 ၁ =ix) ,io+ ]၃၀-၁ []၁၁ ]၉၀+၁ = (၂) ၀၁ + F]galow ux ၁ + [၃]၁
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
![23 of 25
Find the general solution of the system X'(t) = AX(t) for the given matrix A.
A=
OX(t) = C₁e²¹[2] + c₂e¹[] OX(t) = C₁6²1 [²] + ₂0 [¹]
10:21[2] + C₂8¹[2] Xx() = C₁8:21[2] + 20¹1]
A
OX(t)=c₁e
24 of 25
Find the eigenvalues of A, and then the eigenvectors that go with them.
8 +31. (-):8-31 08+31 (¹):8-3 - 8+3 (¹):8-³¹ (¹:0) 08+ (¹:³):8-³, (¹;")}
:8-31,
25 of 25
Use the method of undetermined coefficients to determine only the form of a particular solution for the system:
X'(t) = AX(t) + f(t), where A and f(t) are given.
A=[-* 3] -1 = [46]
А
Ox, 1²a+tb+e Oxp = e'a + tb OXp=ta + 4b +4e¹c Xp = e'a + tb + c](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0126b65b-66a1-4930-86a7-96f79222b7bf%2F290c271d-c71b-4ee1-8ad7-657eb6839b63%2Fstk1iqs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:23 of 25
Find the general solution of the system X'(t) = AX(t) for the given matrix A.
A=
OX(t) = C₁e²¹[2] + c₂e¹[] OX(t) = C₁6²1 [²] + ₂0 [¹]
10:21[2] + C₂8¹[2] Xx() = C₁8:21[2] + 20¹1]
A
OX(t)=c₁e
24 of 25
Find the eigenvalues of A, and then the eigenvectors that go with them.
8 +31. (-):8-31 08+31 (¹):8-3 - 8+3 (¹):8-³¹ (¹:0) 08+ (¹:³):8-³, (¹;")}
:8-31,
25 of 25
Use the method of undetermined coefficients to determine only the form of a particular solution for the system:
X'(t) = AX(t) + f(t), where A and f(t) are given.
A=[-* 3] -1 = [46]
А
Ox, 1²a+tb+e Oxp = e'a + tb OXp=ta + 4b +4e¹c Xp = e'a + tb + c
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
