Question

Solve the system:
x' = 4x − y
y' = 5x + 2y

I have worked out eigen values of λ = 3±2i. I am having trouble finding eigen vectors though. I know that (A-λI)v = 0 will get me there, just not sure how to use it fully. As for the solution, I am kind of stumped there too. Any help would be great.

Answer 1

What class is this? just curious

Answer 2

Differential equations for engineers.

Answer 3

I'm in Diff EQ right now as well. I'm a ChmE major obviously. We don't have a class taylored specifically to engineering tho. That's cool.

Answer 4

Sry I haven't gotten to Eigen Vectors yet

Answer 5

:D
Thanks anyway! Good to know I'm not the only one suffering d.e haha

Answer 6

I just had my first test. I feel ya.

Answer 7

x' = 4x − y
y' = 5x + 2y

x' = [4 -1][x]
y' = [5 2 ][y]

find the eigen values and vectors of the solution. The nature of eigen vector will determine the type of solution of the system.

Answer 8

if you have both real and positive eigen value - or real and both negative eigen value ... then you will have noidal sink

if you have one real ... one positive other negative ... you will have saddle

if you have imaginary part, you will have spiral.

Answer 9

http://ocw.mit.edu/courses/mathematics/18-03sc-differential-equations-fall-2011/unit-iv-first-order-systems/qualitative-behavior-phase-portraits/LinPhasePorCursor.html