Bernoulli differential equation

Bernoulli differential equation ( after Jakob Bernoulli ) is a nonlinear ordinary differential equation of the first order of the form

By transforming

They can be on the linear differential equation

Traced.

The equation is not to be confused with the Bernoulli equation of fluid mechanics.

Theorem on the transformation of Bernoulli's differential equation

Be and

A solution of the linear differential equation

Then

The solution of Bernoulli's differential equation

Next has the Bernoulli differential equation for each trivially as a solution for.

Evidence

It is

Is trivially satisfied while the initial value.

Example: Logistic differential equation

The logistic differential equation

Is a Bernoulli differential equation. Solving therefore

Results

As for all with

Is

The solution to the above equation.