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

https://drive.google.com/file/d/15D2K...

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