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Find a general solution to the system below. 12 -8 8-4 x' (t) = x(t) This system has a repeated eigenvalue and one linearly independent eigenvector. To find a general solution, first obtain a nontrivial solution x, (t). Then, to obtain a second linearly independent solution, try x₂(t) = teu₁ + eu₂. where r is the eigenvalue of the matrix and u, is a corresponding eigenvector. Use the equation (A-ri)u₂u₁ to find the vector u₂. GCZE X(t) = (Do not use d. D. e. Ei, or I as arbitrary constants since these letters already have defined meanings.)

Find a general solution to the system below. 12 -8 8-4 x' (t) = x(t) This system has a repeated eigenvalue and one linearly independent eigenvector. To find a general solution, first obtain a nontrivial solution x, (t). Then, to obtain a second linearly independent solution, try x₂(t) = teu₁ + eu₂. where r is the eigenvalue of the matrix and u, is a corresponding eigenvector. Use the equation (A-ri)u₂u₁ to find the vector u₂. GCZE X(t) = (Do not use d. D. e. Ei, or I as arbitrary constants since these letters already have defined meanings.)

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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Find a general solution to the system below. 12 -8 8-4 x'(t)= x(t) This system has a repeated eigenvalue and one linearly independent eigenvector. To find a general solution, first obtain a nontrivial solution x, (t). Then, to obtain a second linearly independent solution, try x₂ (t)= teu₁ + e^u₂. where r is the eigenvalue of the matrix and u, is a corresponding eigenvector. Use the equation (A-I)u₂ − u₂ to find the vector u₂ x(t) = (Do not use d. D. e. E. i. or I as arbitrary constants since these letters already have defined meanings.)
Transcribed Image Text:Find a general solution to the system below. 12 -8 8-4 x'(t)= x(t) This system has a repeated eigenvalue and one linearly independent eigenvector. To find a general solution, first obtain a nontrivial solution x, (t). Then, to obtain a second linearly independent solution, try x₂ (t)= teu₁ + e^u₂. where r is the eigenvalue of the matrix and u, is a corresponding eigenvector. Use the equation (A-I)u₂ − u₂ to find the vector u₂ x(t) = (Do not use d. D. e. E. i. or I as arbitrary constants since these letters already have defined meanings.)
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