I've only begun to study exact equations so this question will be naive.
I've went through the process of taking a given differential equation, showing that it's an exact equation and hence the derivative of some function $\psi$. Figuring out the function $\psi$ is supposed to be a solution but I don't understand what is actually solved. If I know $\psi$, what information do I have that I didn't have when I only had the differential equation? What can I do with $\psi$?