# solving system of differential equations and eigenvalues

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(See attached file for full problem description)

1) The slope field for the system

dx/dt = 2x + 6y

dy/dt = 2x - 2y

is shown to the right

a) determine the type of the equilibrium point at the origin.

b) calculate all straight-line solution.

2) show that a matrix of the form A =(a b; -b a) with b!=0 must have complex eigenvalues.

3) Let A = (a b; c d), define the trace of A to be tr(A) = a +d. show that A has only one eignevlue if and only if

(tr(A))^2 - 4det(A) = 0

https://brainmass.com/math/linear-algebra/78180

#### Solution Summary

The solution shows how to solve the system of differential equations. Furthermore, it characterizes the equilibrium at the origin.

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