This may be vague, so I apologize. I am interested in applied mathematics, so my question is about the process a scientist or engineer uses to determine what differential equation to use for a non-linear process. I am not familiar enough with describing non-linear processes to be able to give you an example, but from what I hear, nonlinear processes are everywhere around us. I have also read that a linear process's inputs are proportional to their outputs, and that they follow the superposition rule. So, If I were to collect some experimental values on something like testing the height of a wave produced by different sized boats, I could develop a graph of height vs boat hull size. How would I determine if the data collected were linear or nonlinear? If nonlinear, regardless of the differential equation used, how would I transform this into a linear set of equations. So, my question is what constraints have to be met to make a nonlinear process linear? And what effect, does the number of variables play in this analysis?