Question

dx/dt = -5x + y , dy/dt = 4x - 2y

Answer 1

Solution:

Given system is

This system can be expressed as

compare it with

we have

Now, eigen values of are given by

Now, eigen vector corresponding to is given by

if we choose , we get unit vector

Now, eigen vector corresponding to is given by

if we choose  , we get unit vector

Now, the general solution is given by

which is the required solution.

this complete the solution.