Phase Plane & Time Plots for 2-dimensional Linear ODE's
by Mike Martin

On this page, stream plots and a solution curve are generated for the phase plane associated with a system of two 1st-order autonomous, linear, constant-coefficient homogeneous ordinary differential equations. Plots of the solution curves as functions of time are given below the phase plane, too. The equations are of the form:

x ' (t) = x (t) + y (t)

y ' (t) = x (t) + y (t)

x (0) =
y (0) =

The user inputs values of the equation's coefficients. Also, gird bounds, time bounds, and the initial conditions must be specified. The solution to this IVP is solved in both forward and backward time, depending on the time interval entered. The small black point in the phase plane and red points in the x, & y plots indicate the initial condition positions.

Enter in the value of the parameters (above) and select the plotting bounds (below), then press the "Plot/Evaluate" button.

  ≤   t   ≤  

  ≤   x   ≤  

  ≤   y   ≤  


Wikipedia's Phase Portrait

MathWorld's Phase Portrait

DFIELD & PPLANE -- web utilities

Community of Ordinary Differential Equations Educators