WOLFRAM NOTEBOOK

WOLFRAM|DEMONSTRATIONS PROJECT

Homogeneous Linear System of Coupled Differential Equations

​
matrix entries
a
0.5
b
-0.75
c
0.1
d
0.5
′
x
′
y
=
0.5
-0.75
0.1
0.5
x
y
λ
1
= 0.50+0.27
λ
2
= 0.50-0.27
ν
1
=
0.94+0.00
0.00-0.34
ν
2
=
0.94+0.00
0.00+0.34
​
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
x'=0
and
y'=0
. 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
x
and
y
solutions. A variety of behaviors is possible, including that the solutions converge to the origin, diverge from it, or spiral around it.
Wolfram Cloud

You are using a browser not supported by the Wolfram Cloud

Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.


I understand and wish to continue anyway »

You are using a browser not supported by the Wolfram Cloud. Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.