How are differential equations developed


by JaredPM
Tags: developed, differential, equations
JaredPM
JaredPM is offline
#1
Jun16-12, 10:01 AM
P: 15
When differential equations are being developed, what dictates the order of the differential? What decides if it is second order, third order, fourth order, fifth order, etc...
I understand that the process is taking the derivative of a derivative of a derivative, but what decides if the the third, fourth, or fifth derivative has any value when performing the analysis of process being investigated?
Phys.Org News Partner Science news on Phys.org
Simplicity is key to co-operative robots
Chemical vapor deposition used to grow atomic layer materials on top of each other
Earliest ancestor of land herbivores discovered
HallsofIvy
HallsofIvy is offline
#2
Jun16-12, 12:49 PM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,879
It depends upon what the derivative is supposed to represent. "Dynamics" problems, about motion, depend upon "F= ma" and acceleration, a, is the second derivative of the position function so if the problem is to determine position from a given force function, the differential equations are typically second order. On the other hand, problems involving just "growth" or "rate of flow", because those are just "rate of change", tend to be first order differential equations.

Problems involving "elasticity", on the other hand, but again from physical reasons tend to be fourth order equations.


Register to reply

Related Discussions
Writing Linear Differential Equations as Matrix Differential equations Calculus & Beyond Homework 1
United States Elementary Differential Equations - 1st Order Differential Equations Calculus & Beyond Homework 1
A good book on Differential Equations and Partial Differential Equations? Science & Math Textbook Listings 1
Minimal Surfaces, Differential Geometry, and Partial Differential Equations General Math 0
Partial Differential Equations, Applied Nonlinear Equations, and Classical Mechanics Science & Math Textbook Listings 0