2.2 Separable Differential Equation

The first general first-order differential equation is

$$\frac{dy}{dt} = f(x ,y)$$

To identify this class of equation , we write in this form

$$M(x, y) + N(x ,y)\frac{dy}{dx} = 0$$

When$M$is a function o f $x$only and$N$is a function of $y$ ,the equation becomes

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

and we can $\int M(x)dx + N(y)dy = \int 0 dx$