WOLFRAM|DEMONSTRATIONS PROJECT

Bernoulli's Differential Equation

​
equation
x
′
y
(x)+y(x)-x
2
y(x)
c
0
x
′
y
(x)+y(x)-x
2
y(x)
z(x)-x
′
z
(x)-x
Bernoulli's differential equation has the form
y'+P(x)y=Q(x)
n
y
where
n≠0
or
1
.
Dividing by
n
y
, we get
-n
y
y'+P(x)
1-n
y
=Q(x)
.
Substituting
z=
1-n
y
and
z'=(1-n)
-n
y
y'
, we get the linear differential equation
z'/(1-n)+P(x)z=Q(x)
.
This Demonstration shows Bernoulli's equation and solutions for a few choices of
P(x)
and
Q(x)
. Each equation has a family of solutions parametrized by the parameter
c
.