Functions of more than one variable nomenclature

[Calpalned]

Homework Statement

Homework Equations

n/a

The Attempt at a Solution

$y'=f(x.y)$ is a function of two variables. $y=y(x)$ is a function of only one variable. How can they be related? Clearly $y(x) = f(x) \neq f(x,y)$
Thanks

 

[Calpalned]

Perhaps $f(x) \neq y(x)$

 

[Mark44]

Homework Statement

View attachment 90522

Homework Equations

n/a

The Attempt at a Solution

$y'=f(x.y)$ is a function of two variables. $y=y(x)$ is a function of only one variable. How can they be related? Clearly $y(x) = f(x) \neq f(x,y)$
Thanks

The right side of the differential equation y' = f(x, y) involves expressions in both x and y. For example, something like y' = 2x + 3y. Here f is a function that maps a pair of numbers (x, y) to 2x + 3y.

We generally assume that y is related to x in some way.

Perhaps $f(x) \neq y(x)$

Correct.