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.
In general, the solution to a Bernoulli equation will consist of branches, where is the degree of in the equation.
Here is an example of a Bernoulli equation with
. The solution has four branches.