# Bernoulli differential equation

From Calculus

## Definition

In normalized form, this first-order first-degree differential equation looks like:

where . (Note that the cases give first-order linear differential equations).

### Solution method and formula

Divide both sides by . If , this means that we may be potentially discarding the stationary solution , and must remember to add that back to the solution family at the end.

We get:

Now put to get:

Multiply by to get:

This is now a first-order linear differential equation in , and can be solved to get a family of functional solutions for in terms of . Plugging back gives a family of functional solutions for in terms of . We can now add back .