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Showing that a parametised curve is a solution to a system of coupled DE equations

  1. Feb 26, 2012 #1
    Consider a system of coupled differential equations

    x'=5x-y where x(0) = 6
    y'=-x+5y where y(0)=-4

    a) Show that the parametrised curve (x,y)= r(t)=(exp(4t) + 5exp(6t), exp(4t) - 5exp(6t))

    How would you go about showing this?
     
  2. jcsd
  3. Feb 27, 2012 #2
    Re: Showing that a parametised curve is a solution to a system of coupled DE equation

    You just substitute them into the DEs. Keep in mind that x' is really dx/dt and y' is dy/dt. Ok then, differentiate the solutions, put them on the left sides, then substitute the solutions for x(t) and y(t) on the right and see if they're equal.
     
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