# Bernoulli's Differential Equation

Bernoulli's Differential Equation

Bernoulli's differential equation has the form where or .

y'+P(x)y=Q(x)

n

y

n≠0

1

Dividing by , we get y'+P(x)=Q(x).

n

y

-n

y

1-n

y

Substituting and , we get the linear differential equation .

z=

1-n

y

z'=(1-n)y'

-n

y

z'/(1-n)+P(x)z=Q(x)

This Demonstration shows Bernoulli's equation and solutions for a few choices of and . Each equation has a family of solutions parametrized by the parameter .

P(x)

Q(x)

c