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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
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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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
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
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