# Repeated eigenvalues+ differential equation

dx/dt= -4x -y

dy/dt= x-2y

x(0)=4 y(0)=1

x(t)=?
y(t)=?

## The Attempt at a Solution

1) find eigenvalues
(x+4)(X+2)+1
X=-3,-3

2)eigenvectors:
(-3-A)(x,y)=(0,0)

eignvector=(-1,1)

i found P to be (-1,0)

4) so i plugged the eigenvector and the P into the solution for repeated eigenvalues in the link above and got C1=1 and C2=-5

5) plugging those values in i got x=4e^(-3t)+(5t)e^(-3t) and y=e^(-3t)-(5t)e^-3t

however when i entered this into the program(igot all the syntax right) my answer is wrong and ive tried it many times

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vela
Staff Emeritus
Homework Helper
Recheck your calculation of ρ. I think you accidentally flipped a sign.

This is how i calculated P

(lambda-AI)=(-1,1)

1 1 = -1
-1 -1 = 1

addded (1) to (2) to get (2)'

1 1 = -1
0 0 = 0
therefore P1+P2=-1
P1= -P2-1

P=[ -1-P2,P2]

setting P2 to zero i get

(-1,0)

vela
Staff Emeritus
Homework Helper
The equation you want to solve is

$$(A-\lambda I) \vec{\rho} = \vec{\eta}$$

not

$$(\lambda I-A) \vec{\rho} = \vec{\eta}$$

Its works Thanks for your help