Differential Equations: Orders Explained

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Homework Help Overview

The discussion revolves around the concept of orders and degrees in differential equations, focusing on the definitions and distinctions between these terms. Participants are exploring how to classify differential equations based on the highest order of derivatives and the powers of the functions involved.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to clarify the definitions of order and degree in the context of differential equations. There are questions about whether the order refers solely to the highest derivative or if it also involves the powers of the functions. Some participants are discussing the implications of these definitions on the classification of equations as linear or nonlinear.

Discussion Status

The discussion is active, with participants confirming each other's understanding and suggesting terminology adjustments. There is a recognition of the need to differentiate between the order of the differential equation and the degree, indicating a productive exploration of the topic.

Contextual Notes

Some participants note that the original post may have used terminology that could lead to confusion, specifically regarding the distinction between "order" and "degree" in the context of differential equations.

tandoorichicken
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Okay! Just making sure I have the concept of orders in differential equations right. So the order refers to the highest order of the derivatives, not the actual functions right?

So a function like y + yy' = ? would be first order, y + y'' would be second order, but something like y^4 +3yy' would still be first order right?
 
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Yep, you've got it.
 
The "order of the functions" (the power that "y" or its derivatives have in the ODE) gives the nonlinear character...

Daniel.
 
I guess it's preferable to talk about the "degree of the ODE" instead of the "order of the function or its derivative". If degree > 1, the ODE is nonlinear.
 
dextercioby said:
The "order of the functions" (the power that "y" or its derivatives have in the ODE) gives the nonlinear character...
That's "degree". Though the original post should have referred to "order of the diffential equation", not "order of the function".
 

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