Definition:First Order Ordinary Differential Equation

Definition
A first order ordinary differential equation is an ordinary differential equation in which any derivatives with respect to the independent variable have order no greater than $$1$$.

The general first order ODE can be written as:
 * $$F \left({x, y, \frac {\mathrm d y} {\mathrm d x}}\right)$$

or, using prime notation:
 * $$F \left({x, y, y^{\prime}}\right)$$

It is convenient, if possible, to present such an equation in the form:
 * $$\frac {\mathrm d y} {\mathrm d x} = f \left({x, y}\right)$$

or:
 * $$y^{\prime} = f \left({x, y}\right)$$