For an equation of the form $$M(x,y)dx + N(x,y)dy = 0$$ to be exact, it is sufficient that $$\frac{\partial M}{\partial y} \neq \frac{\partial N}{\partial x}$$.

When an equation is exact, the general solution can be written as $$\phi(x,y) = C$$.

Such equations can be solved by finding a potential function $$\phi(x,y)$$ such that $$\phi_x = M(x,y)$$ and $$\phi_y = N(x,y)$$.

An exact differential equation requires that $$\frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}$$.