ODE | Repeated eigenvalues explanation and example

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An example of a linear differential equation with a repeated eigenvalue. In this scenario, the typical solution technique does not work, and we explain how fix the problem.
  1. commutant
  2. ordinary differential equation
  3. ODE
  4. linear equation
  5. repeated eigenvalue
  6. ansatz
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Комментарии
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I am not religious but thank God for videos like this!

teamcowgill
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I think there are not very much videos like this in YouTube. Thank you so much, very well explained and you satisfied my intuitions.I'll subscribe.

flyingbirds
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the satisfaction of understanding that is, is... thank you

bilgekyran
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What if we need a general solution? Where do those constants go in the formula???

nvfpv
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So do you have a video where you explain where the 2nd Ansatz comes from? Every time someone explains this stuff online, as far as I've found so far, they skip over this part.

korganrivera
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what if the repeated roots are 3 what would be our solution is it Y(t)=e^(eugenvalue*t) (uA1+wtA2+zt^2A3) where A1, A2, A3 are eugen vectors

ozgurertenoglu
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what happen if we have zero repeated eigenalues? thanks in advance

gasmiboubekeur
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thanks a lot for the video. It really helped me to understand.

mishudhar
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This video seems not to fit in with the other videos of this series, and assumes a bunch of knowledge not assumed in the other videos.

rlhugh