Ecuación diferencial exacta

$$M(x,y)dx+N(x,y)dy=0$$

Es exacta si se cumple:

$$\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}$$

$$\text{Factores de Integración:}$$

$$\frac{1}{N} \left(\frac{\partial M}{\partial_y} - \frac{\partial N}{\partial_x} \right) = f(x) \hspace{2em} u=e^{\int f(x)dx}$$

$$\frac{1}{M} \left(\frac{\partial N}{\partial_x} - \frac{\partial M}{\partial_y} \right) = f(y) \hspace{2em} u=e^{\int f(y)dx}$$