General Solution to a Nonhomogeneous System (Variation of Parameters)

This is a video that goes through each step of using variation of parameters to find a particular solution to the nonhomogeneous system, which can then be used with the general solution to the homogeneous system to finally get the general solution to the nonhomogeneous system.
Corrections:
- I believe I said the fundamental matrix is denoted using ξ (Xi/Ksi), but I did mean either Ψ (psi) or Φ (phi)
- Not sure why I mentioned matrix matrix multiplication at the end. Variation of parameters here only uses matrix vector multiplication for the most part. Undetermined coefficients makes use of matrix matrix multiplication
drive.google.c...
0:00 Fundamental Matrix
1:39 Ψ inverse
6:15 Ψ inverse times g
8:52 integrating Ψ inverse times g
10:10 Ψ times the integral of Ψ inverse times g dt
15:30 General Solution to the Nonhomogeneous System
#linearalgebra #eigenvector #eigenvectors #eigenvalue #eigenvalues #matrix #matrices #differentialequations #systemsofequations #nonhomogeneous #variationofparameters #variation #vector

[@chelseag.3252]

Your voice is so nice and soothing and this video is so straightforward. Thank you so much! 🙏

[@zachin7]

Awesome lesson. Very clean and easy to follow narration 10/10

[@echoside190]

got the final on Monday and was totally lost on this technique until now. Thank you!

[@nomaetamamo6479]

讲得好，明天就考了祝自己好运

[@noravanegas9830]

thank you! I have a final next week you're saving me!

[@strawberrygirl963]

thank you so much i was searching for this question

[@Neel-Joshii]

What would happen if you had only one eigen value, like (lambda-4)^2? Would you still be able to make a fundamental matrix?

[@I-am-king.]

Thank you so much bro

[@Bedoroski]

Really helpful. Thank you

[@howardyang6741]

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[@thehammyb7613]

MVP