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Math Help - ODE with 3 variables and Matlab

  1. #1
    Junior Member
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    Feb 2008
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    ODE with 3 variables and Matlab

    I've been given this questin which is dependant on a previous question that i9 have already completed.

    x' = 0.5x(1(x^2+y^2 )^2)
    y' = 0.5y(1(x^2+y^2 )^2)

    Above already given and curves drawn. Now consider the ODE governing evolution of
    r(t) = x^2 (t) + y^2 (t). Show that

    r' = r - r^3

    it then says to ass t'=1 to complete the system when drawing the solution curve and using quiver function.

    but i am stuck with what to do, do i use chain rule? and if so how would i apply it, i know i have to use the equations for x' and y' substituted in when i have differentiated r(t) but then i dont know how to use r'=r-r^3.
    Last edited by Stylis10; October 19th 2010 at 05:13 AM. Reason: [MATH[/MATH] wasnt working
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