Question

DE Solution to Non-Homogeneous Linear Systems

Answer 1

The non-homog part is wrong and I'm not sure why?

Answer 2

I just did the det(A-Ir)

Answer 3

It's okay, it's a trick my teacher taught me. I'm not sure if my matrix multiplication is the problem

Answer 4

so that's just x particular and I multiplied the fundamental matrix times u

Answer 5

and u' is the inverse fundamental matrix times the non-homog. part of the equation

Answer 6

I am so sorry, I lost.!!! My prof didn't teach me this way. Let's wait for Kanui

Answer 7

In the line containing \(u'\), on the far right, the entry in the second row should have \(3e^t\), not \(3e^{-t}\).

Answer 8

no it's 3e^-t because that's the non-homog. part of the problem

Answer 9

That's not what I meant. Here:
\[u'=-\frac{1}{4}\begin{pmatrix}-\sqrt3e^{-2t}&-e^{-2t}\\
-e^{2t}&\color{red}{\sqrt3e^{2t}}\end{pmatrix}\begin{pmatrix}e^t\\\color{red}{\sqrt3e^{-t}}\end{pmatrix}=-\frac{1}{4}\begin{pmatrix}-\sqrt3e^{-t}-\sqrt3e^{-3t}\\
-e^{3t}+\color{red}{3e^t}\end{pmatrix}\]

Answer 10

you're so right! thanks! this algebra is tedious -.-

Answer 11

You're welcome!