Properties of Exact Differential Equations

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

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

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

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