6.1 First-order differential equations

In MATH101 you encountered differential equations of the form:

$$\frac{dy}{dx}=ky$$

and

$$a\frac{d^{2}y}{dx^{2}}+b\frac{dy}{dx}+cy=0$$

where $a,b,c,k$ are constants. These are respectively first-order and second-order differential equations: the order is the highest derivative of $y$ appearing in the equation. We will consider first-order differential equations of the form

$$\frac{dy}{dx}=g(x,y)$$

where $g(x,y)$ is a function of two variables.