I'm having some trouble solving a simple differential equation, and yes I'm a bit lazy to check my notes.
It's a simple one, here it is : We have that , . Use the fact that when dx/dt≠0.
It's certainly a beginner question but I have a doubt in this case : x'=dx/dt? I guess yes, since otherwise I don't see what could be x'!
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?
In the same way, if you see the notation y', it will usually mean dy/dx, but you have to look at the rest of the problem to see whether the independent variable is in fact x (or it may be t, or some other letter).