Help with 3rd Order DE (r^3)*r''' - kr' = 0

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In summary, the conversation discusses a differential equation that the speaker is trying to solve with the independent variable t. They mention being in the early stages of learning about differential equations and suggest using Laplace transforms or series solutions to solve the equation. They also mention that some differential equations are not solvable using elementary methods, citing the example of the equation provided. Maple is referenced as a potential tool for solving the equation.
  • #1
osnarf
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The equation I'm trying to solve is (r^3) * r ''' - G*m*r' = 0

the independant variable is t.

I'm not far along in DE's yet to know how to go about this but I was bored and trying to derive something and came across it. Thanks for the help
 
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  • #2
I think Laplace transforms might work. The Laplace transform of (r^3) * r ''' could probably found using integration by parts. Another option would be series solutions. Perhaps there are also other way to solve it. Hmmm...It looks like you could also use order reduction.
 
  • #3
A lot of simple looking differential equations are either completely intractable or at least not amenable to elementary methods. Your equation is a good example. Maple gives a solution for it in terms of non-elementary Airy wave functions.
 

FAQ: Help with 3rd Order DE (r^3)*r''' - kr' = 0

What is a third order differential equation?

A third order differential equation is an equation that involves the third derivative of a function. In other words, it is an equation that relates the rate of change of a quantity to the rate of change of its rate of change.

What is the order of this specific differential equation?

This differential equation is a third order differential equation, as indicated by the presence of the third derivative in the equation.

What is the meaning of the constants r and k in this differential equation?

The constant r represents a physical parameter or characteristic of the system being modeled by the differential equation. The constant k is a coefficient that relates the terms in the equation and can also represent a physical parameter or characteristic of the system.

How do you solve this type of differential equation?

There are various methods for solving third order differential equations, including the method of undetermined coefficients, variation of parameters, and using Laplace transforms. Each method requires different steps and techniques, so it is important to determine which method is most appropriate for the specific equation.

What are some real-life applications of third order differential equations?

Third order differential equations are commonly used to model systems in physics, engineering, and biology. For example, they can be used to describe the motion of a mass on a spring, the growth of a population, or the behavior of an electrical circuit. They are also used in areas such as control systems, fluid dynamics, and economics.

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