Question

Rewrite y''+y'+y=0 as a system of first order differential equations. Find the eigenvalues and eigenvectors of the system.

Answer 1

\[\lambda^{2} + \lambda + 1 =0\]
solve it

Answer 2

Is it \[\lambda= +/- \sqrt{-3/4}-1/2 \] ?

Answer 3

correct
those are the eigenvalues
\[-\frac{ 1 }{ 2 }\pm \frac{ i \sqrt{3} }{ 2 }\]

can you put them in sin and cos form to get the eigenvectors

Answer 4

I'm not sure, could you walk me through it?

Answer 5

are the sin and cos forms \[e ^{-1/2t}(\cos \sqrt{3}/2t + i \sin \sqrt{3/2}t)\]
and

\[e ^{-1/2t}(\cos \sqrt{3}/2t - i \sin \sqrt{3/2}t)\]
?

Answer 6

\[y(t) = e^{-1/2t}(c1*\cos(\sqrt{3}/2)+c2*\sin(\sqrt{3}/2))\]

Answer 7

ok, i think I see that

Answer 8

Is y(t) our eigenvector here?

Answer 9

yup

site is too slow!

Answer 10

lol, I had to wait an hour earlier this morning to get on. Thanks for your help, I really appreciate it :)

Answer 11

no problem.
btw are you engineer?

Answer 12

yes, mechanical. I'm a 3rd year.

Answer 13

im electrical :)

Answer 14

cool :) what year? or have you graduated already?

Answer 15

my 2nd yr in masters