Functions of more than one variable nomenclature

  • Thread starter Calpalned
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Homework Statement


upload_2015-10-20_19-48-36.png


Homework Equations


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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
 

Answers and Replies

  • #3
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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.
 

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