Trajectories of a linear system first order diff. equations

  • Thread starter Nikitin
  • Start date
  • #1
728
27
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! :)
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,847
966
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.
 

Related Threads on Trajectories of a linear system first order diff. equations

  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
12
Views
747
Replies
9
Views
7K
Replies
3
Views
1K
Replies
3
Views
2K
  • Last Post
Replies
2
Views
3K
Replies
5
Views
1K
Replies
9
Views
2K
Top