Solving First order differential equations using matrix methods
I have been trying to solve this equation using matrix methods to find the general solution for x1(t) and x2(t)
(There should be a dot above the x1, x2 to show first order)
x1 = 4x1+ 7x2
x2 = -6x1-9x2
Now i have been shown how to do a second order question so i have used a similar method with this which gets me to this point.
det (a-lambda^2I) = (4-lambda^2)(-9-lambda^2)+42
lambda^2 = -2 and lambda^2=-3
This is where its different to the question i have been through
As this would mean lambda is j1.414 and j1.732
The second order question i have been through comes out with lambda +or- 2j and +or- j which is then obvious how to continue.
Could somone point me in the right direction or to where ive gone wrong?
I have an exam on wednesday and realy need to be able to work with any combination of question they give me, It could be first or second order.
I didnt think it mattered which kind i was until differentiating the general solution part.