So I'm trying to solve this partially decoupled system:
1.) Solve it WITHOUT using matrices. (HINT: start with the second equation)
2.) Solve it with using matrices.
I can do #2... but #1 is so hard.
For #2, I set up the system into a matrix so I get X' = AX, with A being:
Then, I found the eigenvalues:
And the corresponding eigenvectors (call them , respectively:
k_1 = [,], k_2 = [[1/2],
So then the solution is:
Now for #1...
So solving the 2nd equation first...:
Solve for y (I ignored the absolute value so I don't get 2 diff soln's):
So now plug this into 1st eq.:
No idea how to solve this! Maybe I did something wrong.. no idea.