Homogeneous System of Three Coupled, First-Order, Linear Differential Equations

initial conditions

x

1

(0)

1

x

2

(0)

-2

x

3

(0)

1

d

x

1

(t)

dt

d

x

2

(t)

dt

d

x

3

(t)

dt

=

0	-1	2
2	-3	2
3	-3	1

x

1

(t)

x

2

(t)

x

3

(t)

,

x

1

(0)

x

2

(0)

x

3

(0)

=

1

-2

1

x

1

(t)

x

2

(t)

x

3

(t)

= -3

-1

0

1

-2t



+ -6

1

0

-t



+ 4

1

t



This Demonstration calculates the eigenvalues and eigenvectors of a linear homogeneous system and finds the constant coefficients of the system for a particular solution. The sliders let you vary the initial conditions.