# Homogeneous Linear System of Coupled Differential Equations

Homogeneous Linear System of Coupled Differential Equations

This Demonstration shows the solution paths, critical point, eigenvalues, and eigenvectors for the following system of homogeneous first-order coupled equations:

x'=ax+by

y'=cx+dy

The origin is the critical point of the system, where and . You can track the path of the solution passing through a point by dragging the locator. This is not a plot in time like a typical vector path; rather it follows the and solutions. A variety of behaviors is possible, including that the solutions converge to the origin, diverge from it, or spiral around it.

x'=0

y'=0

x

y