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Consider the differential equations dx dt 4x+y+z dy dt = 2x + 5y + 4z dz = -x-y dr Show that if it is assumed that there are solutions of the form x = ae¹¹, y = Bet and z= yet then the system of equations can be transformed into the eigenvalue problem 4 1 α α 2 5 4 BAB 3 11 -10 Y Show that the eigenvalues for this problem are 5, 3 and 1, and find the eigenvectors corresponding to the smallest eigenvalue.

Consider the differential equations dx dt 4x+y+z dy dt = 2x + 5y + 4z dz = -x-y dr Show that if it is assumed that there are solutions of the form x = ae¹¹, y = Bet and z= yet then the system of equations can be transformed into the eigenvalue problem 4 1 α α 2 5 4 BAB 3 11 -10 Y Show that the eigenvalues for this problem are 5, 3 and 1, and find the eigenvectors corresponding to the smallest eigenvalue.

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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Consider the differential equations d.x dt = 4x+y+z dy = 2x + 5y + 4z = -x-y Show that if it is assumed that there are solutions of the form x = ae¹, y = ße^ and z = ye¹ then the system of equations can be transformed into the eigenvalue problem 4 1 α α 2 5 4 BAB 32 -1 -1 Show that the eigenvalues for this problem are 5, 3 and 1, and find the eigenvectors corresponding to the smallest eigenvalue. ele ele ele dz dt
Transcribed Image Text:Consider the differential equations d.x dt = 4x+y+z dy = 2x + 5y + 4z = -x-y Show that if it is assumed that there are solutions of the form x = ae¹, y = ße^ and z = ye¹ then the system of equations can be transformed into the eigenvalue problem 4 1 α α 2 5 4 BAB 32 -1 -1 Show that the eigenvalues for this problem are 5, 3 and 1, and find the eigenvectors corresponding to the smallest eigenvalue. ele ele ele dz dt
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