An example of a nonlinear third-order differential equation in normal form is _______________.

Let’s break down this question. What does it take to make an equation nonlinear? An equation is nonlinear if the graph does not form a straight line. A easiest example of a nonlinear equation includes a trigonometric function such as sin(y) or cos(y).

What makes a differential equation third order? The highest derivative of the equation must be 3. Examples of seeing it written would be y”’ or  d3y/dx3.

Thus, an example of a nonlinear third-order differential equation in normal form is:

\f[\frac{\partial^3y }{\partial x^3}=xsin(y)\f]

Definitions and examples that I used to complete this post can be found in our textbook, chapter 1, section 1. As we move forward in this class, I feel it’s important not to forget our foundations. I am especially guilty of this. I will over complicate problems and become lost. Don’t forget definitions and how things can be broken down.