23 of 25Find 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]AOX(t)=c₁e24 of 25Find 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 25Use 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]АOx, 1²a+tb+e Oxp = e'a + tb OXp=ta + 4b +4e¹c Xp = e'a + tb + c

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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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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