Question

Solve the system of first order linear equations :(

Y'={{-1,2},{-1,-4}}Y
With initial conditions
Y(0)={-1,7}

Please help if you can! Thank you very much :)))

Answer 1

Note: these are first order linear DIFFERENTIAL equations

Answer 2

\[{\bf{y}'}=\begin{pmatrix}-1&2\\-1&-4\end{pmatrix}{\bf{y}}\]
Find your eigenvectors first:
\[\begin{align*}\begin{vmatrix}-1-\lambda&2\\-1&-4-\lambda\end{vmatrix}&=0\\\\
(1+\lambda)(4+\lambda)+2&=0\\\\
\lambda^2+5\lambda+6&=0\\\\
(\lambda+3)(\lambda+2)&=0\\\\
\lambda_1=-3,&\lambda_2=-2
\end{align*}\]
There are your eigenvalues, do you know how to find the eigenvectors?

Answer 3

Yeah got the eigen values working toward the eigen vectors currently.

Answer 4

Having trouble with it, I presume?

Answer 5

Nah I think I'm good at this point, haha thanks for the hand. Honestly just got bored working on an assignment and randomly stumbled on this link. Usually these real time answer submission forum type things are very limited and you almost never get an answer. Figured I'd try submitting the current problem I had to see if It would yield a response. Sorry for the dishonesty but can I award you points or something?

Answer 6

Well at least you're honest about your dishonesty, right? haha, there's that button there if you think I deserve it. Take it easy.

Answer 7

Yeah man, what are you studying by the way. You're ripping through some of these questions.

Answer 8

I'm currently a math major with a minor in bio.

Answer 9

Oh cool man, well have a good one!