Exact Equation
is exact if for some , so the level sets of are solutions.
Definition 5.3 (Exact Equations)
The ODE Equation 1 is called exact if is an exact differential, i.e. there exists a function such that
In particular, if Equation 1 is exact, then and being a constant is a solution.
Example
For , one has . Integrating and matching yields the implicit solution .
Related
Stated in
- Definition 5.3 (Exact Equations)§5.2 Exact equations