Mathematica Tutorial

Bernoulli Equations

A Bernoulli equation is a first-order equation of the form

The problem of solving equations of this type was posed by James Bernoulli in 1695. A year later, in 1696, G. Leibniz showed that it can be reduced to a linear equation by a change of variable.

Here is an example of a Bernoulli equation.

This verifies that the solution is correct.

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Out[3]=

In general, the solution to a Bernoulli equation will consist of n-1 branches, where n is the degree of y (x) in the equation.

Here is an example of a Bernoulli equation with n=5. The solution has four branches.

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Out[4]=