# First order differential equations

Contents

Differential equations with only first derivatives.

How is a differential equation different from a regular one? Well, the solution is a function (or a class of functions), not a number. How do you like me now (that is what the differential equation would say in response to your shock)!

Arguably the 'easiest' class of differential equations. Here we use our powers of algebra to "separate" the y's from the x's on two different sides of the equation and then we just integrate!

Now that you know how to find solutions to separable differential equations, we can use this skill to model some real world phenomena like population growth and how things might cool down.

Can population grow exponentially forever? Malthus would say "no". Well how do you model that mathematically. The logistic differential equation and logistic function are there to rescue us!

Most differential equations cannot be solved by "hand" (through analytical means). However, this doesn't mean that we have to give up! As we'll see in this tutorial, we can use numerical methods to approximate a solution to a differential equation. In particular, we'll learn about Euler's Method which is a fairly intuitive way to do this!

A very special class of often non-linear differential equations. If you know a bit about partial derivatives, this tutorial will help you know how to 'exactly' solve these!

In this equations, all of the fat is fully mixed in so it doesn't collect at the top. No (that would be homogenized equations).
Actually, the term "homogeneous" is way overused in differential equations. In this tutorial, we'll look at equations of the form y'=(F(y/x)).