How to solve Bernoulli differential equations:
- Put the differential equation in the form of Bernoulli’s equation
- Divide by
- Put the equation in the form
- We do this because we set
- We learned how to do this in a previous post
We will solve the first example step by step (click here):
1. Put the differential equation in the form of Bernoulli’s equation
2. Divide by
3. Put the equation in the form
4. Solve linear first order differential equation
Here’s another example (click here):
As long as you memorize Bernoulli’s equation, the equation in Step 3, and how to solve linear first order differential equations, Bernoulli differential equations should be a piece of cake, even if they do take a long time to solve.
Fun fact: Jacob Bernoulli, who found Bernoulli’s equation, is brothers with Johann Bernoulli, who supposedly discovered L’Hopital’s rule. The Bernoulli family had many brilliant mathematicians.
Until next time,