## Example of Exact Equations
Solve the Equation


Let:
> []


Consider the First Order Partials
Thus the equation is exact, and so we know that there must exist some function $f(x,y) = c$ such that:


So first partially integrate $M(x,y)$ in order to find the class of function corresponding to $f(x,y)$:

Now Partially Differentiate $f(x,y)$ to get $N(x,y)$:

Now Equate the Terms:


State $f(x,y)$:


This is merely an implicit solution, but ideally we would want an explicit solution: