Identifying Linearity in Differential Equations: ODE vs. PDE

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Discussion Overview

The discussion revolves around identifying whether a given nth order differential equation, specifically both ordinary differential equations (ODE) and partial differential equations (PDE), is linear or not. Participants explore the criteria that define linearity in these equations.

Discussion Character

  • Conceptual clarification

Main Points Raised

  • One participant inquires about the criteria for determining the linearity of nth order differential equations.
  • Another participant proposes that a differential equation is linear if there are no products of the function and its derivatives, and if neither the function nor its derivatives occur at any power other than the first power.
  • A subsequent reply confirms the correctness of this proposal.
  • Another participant suggests looking at the definition of "linear differential equation," indicating that they believe the initial inquiry has been addressed satisfactorily.

Areas of Agreement / Disagreement

There appears to be agreement on the criteria for linearity as proposed by one participant, but the discussion does not explore any additional conditions or alternative viewpoints, leaving some aspects potentially unresolved.

Contextual Notes

The discussion does not delve into any missing assumptions or definitions that may be relevant to the criteria for linearity in differential equations.

jason.bourne
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how do i know a given nth order differential equation is linear or not?
both for ODE as well as PDE.
 
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okay i figured it out.
there should not be product of function and its derivatives
neither the function nor its derivatives occur at any power other than the first power.

m i right?
or are there any other conditions other than these?
 
You are right.
 
I was going to suggest that you look at the definition of "linear differential equation"! I am pleased that you have already done that!
 

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