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Trajectories of a linear system first order diff. equations

  1. Apr 14, 2013 #1
    In linear algebra, you can have systems of differential equations represented by matrices.

    What does a "trajectory graph" of such a system show, exactly? And how can you draw one?

    What's the difference between such a trajectory-graph and an ordinary slope-field for a single linear differential equation?

    Thanks! :)
     
  2. jcsd
  3. Apr 14, 2013 #2

    HallsofIvy

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    The "slope field" is a graph showing short straight lines at each (x, y) point (well, in reality as many as possible without one covering another!), showing the slope of a solution to the differential equation. A "trajectory graph" is a graph showing an number of actuals "trajectories" (solutions) of the differential equation, with different initial conditions as possible.

    If you have a "slope field" for a differential equation, each of the trajectories must be parallel to the slope field lines at each point.
     
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