# Dif.equation system

1. Oct 21, 2013

### prehisto

1. The problem statement, all variables and given/known data
System1:
dx/dt=x+y
dy/dt=8x-y

2. Relevant equations

3. The attempt at a solution
detreminant=(1-λ)(-1-λ)=(λ-3)(λ+3);λ$_{1}$=-3 and λ$_{2}$=3

So system 2:
(1-λ)$\alpha$+$\beta$=0
8$\alpha$+(-1-λ)$\beta$=0

When i put λ$_{1}$=-3 in system 2 -> $\alpha$ and $\beta$=0.
the same goes for λ$_{2}$

That menas that solution in form of y=C_1*$\beta$_1*exp(λ$_{1}$*t)+C_2*$\beta$_2*exp(λ$_{2}$*t) is equal to 0. Thats wrong.

Where is my mistake?

Last edited by a moderator: Oct 21, 2013
2. Oct 21, 2013

### tiny-tim

hi prehisto!

so far so good! …
now solve either line to get β = 2α, so your eigenvector is any multiple of x + 2y

3. Oct 21, 2013

### prehisto

ok,that means that i can chose α1=1 β1=2 and
α2=1 β2=-4

y=C11*exp(λ1*t)+C22*exp(λ2*t)
x=C11*exp(λ1*t)+C22*exp(λ2*t)
Is this form of solution correct or I have to use something else?

4. Oct 21, 2013

### tiny-tim

i think it would be better if you checked by starting with the eigenvector equations

x + 2y = Ae3t
x - 4y = Ae-3t