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Math Help - DE system with a condition

  1. #1
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    DE system with a condition

    dx/dt = -ay if x>=0 else 0
    dy/dt = -bx if y>= 0 else 0

    x and y start at xo and yo

    The goal is to find out whether x or y hits 0 first depending on the initial values and the decrement rate. (0,positive) is not an equilibrium point if you ignore the conditionals so I'm not sure what to do here.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by bob000 View Post
    dx/dt = -ay if x>=0 else 0
    dy/dt = -bx if y>= 0 else 0

    x and y start at xo and yo

    The goal is to find out whether x or y hits 0 first depending on the initial values and the decrement rate. (0,positive) is not an equilibrium point if you ignore the conditionals so I'm not sure what to do here.
    Why not solve them without the constraints, then find the first time either of them becomes zero, and from that point on the solution to the constrained problem is constant (and up to that point is equal to the solution of the unconstrained problem).

    CB
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