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# seperating the variables watch

1. so i have dyx = y^2 dx, and i need to seperate the variables. which way do i go?

dy/y^2 = dx/x

or

x/dx = y^2/dy

i'm guessing the second one, but how do i know? can i do either?
2. The first one

You can't 'divide' by a dx (or dy) as far as I'm aware.
3. yep the first one
4. thanks guys!
5. (Original post by EierVonSatan)
You can't 'divide' by a dx (or dy) as far as I'm aware.
Sorry if I'm being very silly, but isn't that what differentiation is?
6. (Original post by meatball893)
Sorry if I'm being very silly, but isn't that what differentiation is?
It's a bit like this:

d/dx= differentiate with respect to x
7. (Original post by EierVonSatan)
The first one

You can't 'divide' by a dx (or dy) as far as I'm aware.
Well.

In this sense, "dx" and "dy" don't really mean much anyway. The notation is very conveniently set up to allow completely meaningless statements like "dy/y^2 = dx/x" to work exactly as you'd expect them to and still at the end translate into something meaningful. The sentence "y^2/dy = x/dx" makes about as much sense as "dy/y^2 = dx/x" (i.e. it doesn't, but it can be transformed into something that does and is true), it just so happens that sticking integral signs in front of the former (which is what we ultimately what to do) still doesn't make it make sense. So we always do the latter.

Edit: oh, and incidentally, if you do divide by dx, you get (dy/dx)/y^2 = x, which makes perfect sense (and is again true).
8. (Original post by generalebriety)
Well.

In this sense, "dx" and "dy" don't really mean much anyway. The notation is very conveniently set up to allow completely meaningless statements like "dy/y^2 = dx/x" to work exactly as you'd expect them to and still at the end translate into something meaningful. The sentence "y^2/dy = x/dx" makes about as much sense as "dy/y^2 = dx/x" (i.e. it doesn't, but it can be transformed into something that does and is true), it just so happens that sticking integral signs in front of the former (which is what we ultimately what to do) still doesn't make it make sense. So we always do the latter.
I knew I'd be hauled up for that

Separation of variables is (as my maths friends tell me) quite complicated and I don't pretend to know that much about it

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