possessive forms

[mamen]

Do the following phrases imply the same thing:

"functions' equation" and "functions equation";

"function's equation" and "functions equation"?

[mamen]

Do the following phrases imply the same thing:

"The functions' equation is linear." and "The functions equation is linear.";

"The function's equation is linear." and "The functions equation is linear."?

help.......

[5jj]

Please use the phrase(s) in a complete sentence. It is difficult to say what is possible or not when we have only two words.

[mamen]

Please use the phrase(s) in a complete sentence. It is difficult to say what is possible or not when we have only two words.

I have just edited it sir...

[bhaisahab]

"The function's equation is linear." This is grammatical.

[Abstract Idea]

help.......

Although grammatical as Bhaisahab says, to me it looks a bit strange, maybe of a poor style, let us say.

Why not say it simpler as "The function is linear" or "This is a linear function" ?

I am with 5jj and would like more context here.