Direction Fields for Differential Equations

y' = a (y - b)

y' = (y + a) (y - b)

y' = -(y + a) (y - b)

y' = -a + b t - y

y' = -a t + b -

2

y

a

1

b

1

This Demonstration lets you change two parameters in five typical differential equations. Observe the changes in the direction field and long-term behavior of the system. Notice the changes in both the lines of equilibrium and the direction of the field.

References

[1] W. E. Boyce and R. C. DiPrima, Elementary Differential Equations with Boundary Value Problems, 9th ed., New York: John Wiley and Sons, 2008.

External Links

Differential Equation (Wolfram MathWorld)

Direction Fields

Permanent Citation

Stephen Wilkerson

"Direction Fields for Differential Equations"
http://demonstrations.wolfram.com/DirectionFieldsForDifferentialEquations/
Wolfram Demonstrations Project
Published: August 10, 2012