System of first-order linear odes: repeated roots

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Solves a system of two first-order linear odes with constant coefficients using an eigenvalue analysis. The roots of the characteristic equation are repeated.

  1. Jeffrey Chasnov
  2. Differential Equation (Concepts/Theories)
  3. system of equations
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Комментарии
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ODE test tomorrow. The formula in my note make sense now!! THANK YOU SO MUCH!!!

yinggling
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excellent video. It can't get much clearer than how you've put it

dkRun
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4:45 is the pace to start to learn about the second guess to make after finding the eigenvector for the repeated root

TheSacknasty
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Thank you so very much. This was a huge help!

Shadowmeld
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Question: The vector w that was found, is it unique? If u solve the equations in w1 and w2 and solve for w1 in terms of w2 we will end up with w = (-1 0) instead of w = (0 -1). These two are linearly independent which leads me to think that it is not unique

dkRun
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Can you please proof that the second solution x2=(w+tv)e^_lambda (t)

EMEngiALL
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is there a mistake at about 6:53? (ill say lambda = r)
You have A*x where x = (w + tv)e^(rt) then when you times this by the matrix A you only times Aw and not the vector tv, it doesnt actually matter as if you do times tv with A (to get Atv) and doing some rearranging you'll end up with (A-rI)v*te^(rt) but we know that (A-rI)v = 0 as this is how we got r and v

mi
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w1 and w2 can be (-1/2 -1/2) Is this ok or another solution?

BallsonPHACE
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