Families of Solutions for ODEs

dy

dx

=

a

b

x

+c

d

y

a

1

b

1

c

1

d

1

This Demonstration explores families of solutions of an ordinary differential equation (ODE) of the form

dy

dx

=f(x,y)

, which are plotted using the vector field

(1,f(x,y))

. For each choice of

f

you can see how the solutions depend on the value of the parameters; in some cases going from negative to positive values causes a significant change in the behavior of the solutions.