Answered: 1. for the case of repeated real roots…

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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1. for the case of repeated real roots what would the general solution be?

2. if i was to let y1(t) = theta(t) as well as y2(t) = theta'(t)=y1'(t) how could i show that the initial equation could be written as a system of 1st order odes that involved y1 and y2. the system will then need to be presented as a the matrix equation y' = My

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how could i show that the M eigenvalues are equal to the roots computed before (for real repeated)

what is the eigenvector for the case of repeated eigenvalues (should be a single vector) - the matrix and eigenvalues are defective.

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