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Math Help - system of differential equations

  1. #1
    Junior Member
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    Nov 2007
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    system of differential equations

    Does anybody know how to solve the system of differential equations,

    y'(t) = -ay(t) + ax(t)

    x'(t) = ay(t) -ax(t)

    with initial conditions, y(0)=1 and x(0)=0 where a is a real constant and also with y(t) + x(t) = 1 for all t
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  2. #2
    Super Member flyingsquirrel's Avatar
    Joined
    Apr 2008
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    802
    Hi

    Let's use the equations we're given : substitute x(t)=1-y(t) in y'(t)=-ay(t)+ax(t) :

    y'(t)=-ay(t)+a(1-y(t))=-2ay(t)+a

    Hence y is given by the ODE  y'(t)+2ay(t)=a which you can solve. Once you know y, you can use x(t)=1-y(t) to find x.
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