Classification of the equation

[Maximtopsecret]

Homework Statement

Here is the equation:

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...

 

[Ray Vickson]

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?

 

[SteamKing]

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.

 

[Maximtopsecret]

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

Thank You!
I've looked up. Here is something from Wikipedia:

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.

 

[SteamKing]

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.

There is one characteristic about a homogeneous equation, which can be determined by merely glancing at it, however.

 

[Maximtopsecret]

IDK about the Wiki article you read, 'cuz you didn't provide a link.

There is one characteristic about a homogeneous equation, which can be determined by merely glancing at it, however.

Ok, so if we have some g(t) and f(t) in the right part of the eq., then it is inhomogenous, right?

 

[SteamKing]

Ok, so if we have some g(t) and f(t) in the right part of the eq., then it is inhomogenous, right?

Yep.