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

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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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