Solving General High-Order, Linear Ordinary Differential Equations (ODEs)

This video shows how to solve general high-order linear differential equation systems, using the characteristic polynomial and linear superposition.
Playlist: • Engineering Math: Diff...
Course Website: faculty.washington.edu/sbrunto...
@eigensteve on Twitter
eigensteve.com
databookuw.com
%%% CHAPTERS %%%
0:00 Overview
1:56 Guess x(t) = exp(lambda*t) and Plug Into ODE
6:12 Characteristic Polynomial
8:43 The General Solution
11:48 Using Initial Conditions
16:35 It's not a Wronskian!!! (or is it!)

[@saraiva407]

23:20 Maybe it's the Vandermonde matrix?

[@superuser8636]

I really appreciate your candor and humor when dealing with Wronskians 😂

[@ayublakhani3913]

Just got your 2nd edition and it is a goldmine of information. Thank you for the book and all these videos to reinforce the key concepts!

[@ayoadeadeyemi01]

What's the name of the book?

[@akhiljalan11]

The matrix at 23:09 is a Vandermone matrix. en.wikipedia.org/wiki/Vandermonde_matrix

[@hoseinzahedifar1562]

Great and thanks... 👏👏
however, it is the transpose of a Vandermond matrix, not a Vandermond matrix itself...

[@FadoodleX]

@@hoseinzahedifar1562 Math pedantry FTW!

[@alial-ghanimi8357]

I really appreciate your effort. Thanks.

[@juandiego33140]

What a great job! Thanks a lot for sharing

[@hoseinzahedifar1562]

Great Lecture, and thank you...😍😍.

[@rudypieplenbosch6752]

Amazing how straightforward solving a higher order DE actually is, when I see a higher order DE it used to be a scary thing, thanks.

[@martinsanchez-hw4fi]

The characteristic polynomial is the actual hairy thing

[@rushikeshjadhav4103]

Great Explanation....!!!

[@curtpiazza1688]

Cool ! Thanx so much! 😊

[@lioneloddo]

Gauss-Jordan method? The idea being, I guess, to transform first the dense matrix in an equivalent upper triangular matrix or something like this.

[@Alan-zf2tt]

Well I'll be jiggered! @ 10:31 hmmm... eigenvectors and eigenvalues Interesting! Plus on Michael Penn's channel there was an observation along lines of:
if something, say wlog X a poly'l eqn, has a solution in m-space for m

[@ChristianRosenhagen]

Please consider using Σ

[@ST-te8sd]

you are writing from left hand?

[@carultch]

The video is mirrored, and he is left-handed. If you saw him doing this live, you'd see the text reversed.

[@lioneloddo]

But what intellectual prowess! After a few minuts, I can't follow the demo anymore. An then I just see colors, shapes and patterns and a kind of a beautiful music for my frenchy ears ...

[@fabiofarina9579]

different marker, exactly the same squeek :-D

[@sigfridsixsis3255]

Vandermonde matrix

[@sigfridsixsis3255]

And it is ill conditioned