Classification of the equation

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Homework Help Overview

The discussion revolves around classifying a given equation in the context of differential equations, specifically whether it is homogeneous linear, unhomogeneous linear, or quasilinear. Participants are examining the definitions and characteristics of these classifications.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants express their opinions on the classification of the equation as homogeneous linear, while others question the definitions of "linear" and "homogeneous" in the context of partial differential equations. There are references to external sources for clarification.

Discussion Status

The discussion is ongoing, with participants sharing their interpretations and seeking clarification on definitions. Some guidance has been offered regarding the characteristics of homogeneous and inhomogeneous equations, but no consensus has been reached on the classification of the specific equation in question.

Contextual Notes

Participants note the importance of understanding the definitions and characteristics of linearity and homogeneity, with references to external sources such as Wikipedia for additional context. There is an acknowledgment of the need for clarity regarding terms used in the classification.

Maximtopsecret
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Homework Statement


Here is the equation:
Безымянный.png

Homework Equations


What kind of equation is it(homogenous linear, unhomogenous linear, quazilinear...)

The Attempt at a Solution


I suppose it is a homogenous linear one...
 
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Maximtopsecret said:

Homework Statement


Here is the equation:
View attachment 84005

Homework Equations


What kind of equation is it(homogenous linear, unhomogenous linear, quazilinear...)

The Attempt at a Solution


I suppose it is a homogenous linear one...

Define "linear" (in a pde context). Does the equation fit that description?
 
Maximtopsecret said:

Homework Statement


Here is the equation:
View attachment 84005

Homework Equations


What kind of equation is it(homogenous linear, unhomogenous linear, quazilinear...)

The Attempt at a Solution


I suppose it is a homogenous linear one...

Also, look up "homogeneous" in the context of describing equations.

Also, "inhomogeneous" is how to characterize an equation which is not homogeneous, and an equation which is "quasilinear" depends on its particular form.
 
Ray Vickson said:
Define "linear" (in a pde context). Does the equation fit that description?
Thank You!
I've looked up. Here is something from Wikipedia:
Безымянный.png

So, I stick to my opinion it is linear.
But I can't so far decide about it being homogenous... In one Wiki article I read: diff. equation containing non-zero free term in the right part of the equation. This term must be independent on the unknown functions.
 
Maximtopsecret said:
Thank You!
I've looked up. Here is something from Wikipedia:
View attachment 84010
So, I stick to my opinion it is linear.
But I can't so far decide about it being homogenous... In one Wiki article I read: diff. equation containing non-zero free term in the right part of the equation. This term must be independent on the unknown functions.
IDK about the Wiki article you read, 'cuz you didn't provide a link. o_O

There is one characteristic about a homogeneous equation, which can be determined by merely glancing at it, however. :wink:
 
SteamKing said:
IDK about the Wiki article you read, 'cuz you didn't provide a link. o_O

There is one characteristic about a homogeneous equation, which can be determined by merely glancing at it, however. :wink:
Ok, so if we have some g(t) and f(t) in the right part of the eq., then it is inhomogenous, right?
 
Maximtopsecret said:
Ok, so if we have some g(t) and f(t) in the right part of the eq., then it is inhomogenous, right?
Yep.
 
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