Chapter 1: First order ODEs

A first order ODE is an equation of the form

$$\dfrac{dy}{dx}=f(x,y) \nonumber$$

or just

$$y'=f(x,y) \nonumber$$

In general, there is no simple formula or procedure one can follow to find solutions. In the next few lectures we will look at special cases where solutions are not difficult to obtain. In this section, let us assume that $f$ is a function of $x$ alone, that is, the equation is