Thanks Opalg. This notation confuses me. I don't really understand well how it can be solved. Are we looking for a function x(t)? Or just "x"?

Also... well I need to read much more on calculus, but why can we separate the dt from the expression dx/dt? It's not a division...

I think I can solve problems like this one :

and with the same initial condition as I posted at first. But when I have x' in function of x, then I'm lost. (that's why I'm posting here right now).

It's also confusing to me that instead of writing x'(t)=t for example, we just write x'=t.

What I've thought about the problem is

. Now from there should I integrate??? I will have x= something depending of x but with dt at the end. So I guess this is not the way to do it.

Can someone give me a hint solving the differential equation?