- This topic in mathematics is named after Jakob Bernoulli. See Bernoulli's principle for an unrelated topic in fluid dynamics, named after the inventor Daniel Bernoulli.
In mathematics, an ordinary differential equation of the form
is called a Bernoulli differential equation or Bernoulli equation when n≠1, 0. Dividing by yields
A change of variables
is made to transform into a linear first-order differential equation.
The substituted equation can be solved using the integrating factor
Consider the Bernoulli equation
Changing variables gives the equations
which can be solved using the integrating factor
Note that left side is the derivative
. Integrating both sides results in the equations
The solution for