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
.