Classification of the equation

In summary, the conversation discusses an equation and attempts to determine its type (homogeneous linear, inhomogeneous linear, or quasilinear). The equation is described as being linear and potentially homogeneous, but further research is needed to confirm the latter. The conversation also mentions that a characteristic of a homogeneous equation is the absence of a non-zero free term in the right side of the equation.
  • #1
Maximtopsecret
19
0

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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  • #2
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?
 
  • #3
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.
 
  • #4
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.
 
  • #5
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:
 
  • #6
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?
 
  • #7
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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1. What is the purpose of classifying equations?

The purpose of classifying equations is to organize them into different categories based on their properties and characteristics. This makes it easier to identify patterns and relationships between equations, and to apply appropriate methods and techniques for solving them.

2. What are the main types of equations?

The main types of equations are linear, quadratic, polynomial, exponential, logarithmic, and trigonometric. These types can be further divided into subcategories based on their specific properties and features.

3. How do you determine the type of an equation?

The type of an equation can be determined by looking at its highest exponent. For example, an equation with a highest exponent of 1 is linear, while an equation with a highest exponent of 2 is quadratic. Other properties, such as the presence of certain terms or functions, can also help identify the type of an equation.

4. What are the characteristics of a linear equation?

A linear equation is a type of equation with a constant rate of change, meaning that there is a consistent increase or decrease in the dependent variable for every change in the independent variable. It has a maximum of one solution and can be represented by a straight line on a graph.

5. How is the classification of equations useful in real life?

The classification of equations is useful in various fields such as physics, engineering, and economics. It allows us to model and solve real-world problems by identifying the appropriate type of equation and using specific methods to solve it. It also helps us understand the behavior and relationships of different variables in a system.

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