System of differential equations

[@RalphDratman]

This is great. Thanks, Dr. P.
I have never seen anyone quite so enthusiastic about a clever way to solve a math problem.

[@joluju2375]

Okkaaay, all these 0 make calculations more easy, now I see why we would diagonalize. Thank you for opening my eyes.

[@giampiproietti]

My Automation exam included the analysis of dynamic systems. I realized how powerful the matrix representation of the equations for a LTI is. A complete system ruled by multiple linear differential equations can be solved just using linear algebra and laplace transform. I love math

[@benjiusofficial]

Maaaaan, we did that diagonalization a couple quarters ago but I was never told that c1e(eig)t[] + c2e(eig)t[] trick! That would've made stuff waaaaay smoother!

[@Arycke]

A nice connection well put as usual sir. Thank you for the upload! :D

[@michalbotor]

neat! i've never seen it solved using this detailed, making-everything-understandable-and-obvious method. thanks! ;)

[@arongil]

Thanks so much for making these videos. I'm taking Differential Equations now, and I believe next week will involved such systems of differential equations. I'm excited to connect the less intuitive way I'm sure will be presented with your Linear-Algebra-ized method.

[@MoonLight-sw6pc]

Such a great explenation .
Thank u

[@spiritgoldmember7528]

Great work as always!

[@anasjedidi1669]

System of non homogeneous differential equations ?!!

[@Rundas69420]

Does this also work with systems where the diff. eq. have non-constant coefficients? If yes this method is superior to bprp's D-notation.

[@colaurier2594]

Wonderful !

[@sinarzaito1106]

Make a video about Euler's Identity

[@michaelempeigne3519]

What does Picard iteration look like using linear algebra?

[@holyshit922]

Solving system of ode by converting to symmetrical form and using so called first integrals is nice way

[@SefJen]

And how to solve the system if the matrix is not diagonalizable ?

[@drpeyam]

Jordan form

[@CacchiusMan]

I wonder what happens if the matrix is not similar to a diagonal matrix, though... do you use at that point Jordan's canonical form on the complex form of the matrix?

[@drpeyam]

Yep :)

[@borg972]

Can you show how to use this to find a general solution to an non-homogeneous system?

[@drpeyam]

There’s a video on variation of parameters

[@borg972]

Thanks!

[@gustavosedano294]

Amazing!! :0

[@ImPresSiveXD]

Very nice! :D

[@rome8726]

Good

[@Hobbit183]

neat :>

[@mipmip4575]

Linear AlgeBruh