What Is Bernoulli’s Equation?

Overview

The Bernoulli’s equation was introduced by the mathematician Jacob Bernoulli in 1695.

Bernoulli equation is the nonlinear differential equation.

Definition

The equation of the form-

is called the Bernoulli equation.

Here P and Q are constants of x

On dividing the equation (1) by y^n we get-

And putting 

so that

Or

Equation (2) becomes,

Or

Which is properly a linear equation and can be solved easily.

Lets understand the theory by doing an example.

Example-1: Solve-

Solution.

Here we have-

Which is the form of Bernoulli equation,

Now divide the given equation by xy, we get-

Put 

z=log⁡y

So that

Then equation (1) reduces to-

Now

Integrating factor-

The solution will be-

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