about y'

One would say that aloud in English as "y prime." The symbol ' used in a mathematical expression refers to what the American Heritage Dictionary defines as: One used to distinguish different values of the same variable in a mathematical expression.

Thank you very much, Setanta. And so y'=x/y should be read as y prime equals what? That is, I don't know how to read x/y. Could you tell me,please? Thanks.

In differential equations y' is often a shortcut which means dy/dx (read the derivitive of y with respect to x). Sometime (depending on the context) 't' or another 'obvious' independent variable is meant in place of x.

That would be read, if you have expressed it correctly, as: "y prime equals x divided by y." Usually, a "prime" variable is often expressed as follows: "factor in y prime, where y prime equals x divided by y . . . "

Setanta (with all due respect), I think you are mistaken.

I am pretty sure the problem is a differential equation. This is a standard problem in calculus and is really a symbolic shortcut for

dy/dx = x/y

The challenge being to find the set of functions that have this derivative...

I have not offered any mathematical opinions, here, E_brown. The question was how to say the symbols in English, and that is the only topic which i have addressed. The member did not ask for a mathematical solution or description, and i have not offered either.

You are both right. Yes, the equation I provided is y'=x/y, i.e. dy/dx=x/y. I just asked how to read that equation. Now I got it. Thank you both!