The differential equation
where and , is known as the Bernoulli’s equation.
When is an integer, (1) has trivial solution .
To obtain nontrivial solution, we divide each term of (1) by to get,
(2) can be expressed as
Let , (3) is transformed to a first order linear equation
giving the general solution of a Bernoulli’s equation (see Fig. 1)
For a concrete example of Bernoulli’s equation, see “What moves fast, will slow down“