are differentials "dy" and "dx" considered variables?

PG1995

Joined Apr 15, 2011
816
Hi

Please have a look on the attachment. You can find find my question there. Thank you for the help.

Regards
PG

steveb

Joined Jul 3, 2008
2,436
Hi

Please have a look on the attachment. You can find find my question there. Thank you for the help.

Regards
PG
Differentials can be variables, but in this context the x and y are the variables they are talking about that are separable.

thatoneguy

Joined Feb 19, 2009
6,359
Calculus and higher math run on expanding the concept of algebra.

In algebra, a letter can denote any number, it has been found that a letter, say f(x) can represent any equation. The dx and dy components point to the 'working variables' of the function, which can be worked on using calculus formulas.

An example is the forms of integration for a function F(x) if it fits certain models, the integration of such is known, so instead of x=sin(45) in algebra, f(x)=sin(x) dx in calculus, with x being the working variable.

panic mode

Joined Oct 10, 2011
1,829
as others have mentioned, x, y, t etc. are generally used as variables. and in this context they are still variables so you can use math to manipulate them.

suppose you have
dy/dt=k*y*t^2

this is separable because you can separate y and t to get for example:

dy/y=k*t^2*dt

now it is easy to solve because all y are on one side and all t are on other.
but you will not be lucky enough to only deal with separable variables.

but suppose you have

dy/dt +t*y= t^2

as you can see there is a problem, can't just separate them...