Bernoulli differential equation
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.
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 .