Phase portrait

for a system of two linear differential equations

with constant coefficients

This page contains four Java applet contructions. Three of them are Javasketchpad Sketches and the fourth is an InterJSP applet that connects these together.

The upper left Sketch shows a direction field for a linear system. The coefficient matrix is determined by its determinant and trace in the upper right Sketch. Their values can be modified by dragging the point (det,trace) in the plane.

Solving a 2x2 system using only its determinant and trace leaves two of its elements unsolved. These are treated like variables and you can modify them by dragging the points a and c along the lines in the botton left Sketch.

Before you connect these JSPs together, you should wait until both of them have been loaded and press the Connect button in the botton right Sketch.