- #1
KevinD6
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Homework Statement
Y' =
[ -14 0 12
24 -2 24
16 0 14 ] Y
Subject to the condition [itex] y_1 (0) = -6, y_2 (0) = 11, y_3 (0) = 8, find: y_1(t), y_2(t), y_3(t) [/itex]
Homework Equations
The Attempt at a Solution
This is more just to see if my answers are correct than anything, so I begin by finding the eigenvalues of the matrix (checked with an internet calculator so I know this is correct).
Eigenvalues end up being: -2, -2, and 2.
I solve for the eigenvectors, which end up being :
[itex] v_1 = [-1, 0 ,1], v_2 = [0, 1, 0], v_3 = [-3, 6, 4] [/itex]
Therefore I have the general solution: [itex] Y = C_1 v_1 e^{-2t} + C_2 v_2 t e^{-2t} + C_3 v_3 e^{2t} [/itex]
Using the initial values given, putting it into the matrix and solving it, I end up with:
[itex] C_1 = -3,
C_2 = 13/2, C_3 = 4
[/itex]
However, the question wants me to find [itex] y_1 (t), y_2 (t), and y_3 (t) [/itex]
It also does not allow me to enter a vector as an answer, so does anyone know how my answer is supposed to be formatted? Or am I going about it wrong? Thank you for any assistance you may provide.