When and where the exact and non-exact differential equations are to be used?

Exact differential equations are used when a differential equation can be expressed in the form (M(x, y)dx + N(x, y)dy = 0) where (\frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}), allowing a solution via a potential function. Non-exact differential equations, on the other hand, arise when this condition does not hold, necessitating methods such as integrating factors or substitutions to find solutions. Exact equations typically simplify the solving process, while non-exact equations require additional techniques to render them solvable.