8 Differential Equations

We have already discussed derivatives in relation to integrals and related rates but there is a course provided in most universities that focuses solely on differential equations. Differential equations describe the change of an object, a line, space, etc. Anything that changes over time can be defined by a differential equation.

Differential equations go far beyond just taking the derivative of a function. In this course you learned to define different differential equations by their order which equates to the highest derivative in the equation. Consider the following equation

In this example we see that the highest derivative is 3 and thus we describe the differential equation as having an order of 3. Even further we classify different equations as linear or non-linear. Linear equations follow the order of the highest order derivative being farthest to the left and the subsequent term is an order less than the previous. If at any point a smaller order derivative is in front of a higher order derivative then we classify this as a non-linear differential equation.

Branching even further, in the context of linear differential equations we have homogeneous and non-homogeneous equations.

Homogeneous equations can be classified by following the form

Non-Homogeneous equations can be classified by the following form

Throughout the Differential equations course we are using different methods to find solutions for the different types of differential equations classified above.