What is an exact differential equation?
There must be a 0 on the right side of the equation and and must be separated by a +.
Steps to solve exact differential equations:
- Verify that
- Find and
- This will help us find
- Don’t forget to substitute or
First example (click here):
1. Verify that
3. Replace c with
We took the derivative with respect to x of , which is equal to . We then compared the derivative to , the equation we didn’t integrate. We then integrated both sides to solve for .
5. Find the implicit equation
Here’s another example (click here):
Exact differential equations may look scary because of the odd looking symbols and multiple steps. If you double check your work, memorize the steps, and practice, you can definitely get this concept down. Don’t be afraid and dive in!
Until next time,