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System of diff equations

  1. Apr 25, 2005 #1
    I am having problems with solving systems of differential equations.

    x'= [(-3 ) (gamma)]x
    .....[ ( 6 ) ( 4 ) ]

    I am supposed tofind the interval of values of gamma for a) stable focus and b) stable node.

    I started by
    [(-3-r) (gamma)][x1] = [0]
    [( 6 ) (4-r ) ][x2]....[0]

    det(A-rI) = (-3-r)(4-r)-6(gamma) = 0
    = r^2-r-12-6(gamma)= 0

    but I don't know where to go after this point to find these different intervals.

    For another problem:
    x'= [0 3]x
    .....[-12 0] with initial conditions x1(0)= 1, x2(0) = 2

    show that the solution x(t) is periodic and determine its period. Additionally to find the moment(s) when the point x(t) is closest to the equilibrium point 0.

    For this I have
    [(-r ) (3)][x1] = [0]
    [(-12) ( -r)][x2]....[0]
    so r^2 + 36 = 0

    how do I factor this? and after I find my values of r and plug them back in, where do I go?
  2. jcsd
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