What do the primes mean in this differential equation?

[FredericGos]

Hi,

I'm reading an old book titled 'Mathematics of classical and quantum physics' by byron & fuller. It's quite nice, but some of the notation confuses me.

On page 388, they're showing a simple differential equation:

$$-i\frac{dy}{dx}=f(x)$$

fine, but then they write the solution (given the initial condition y(a)=y0) as:

$$y(x) = y0 + i\int_a^x f(x')dx'$$

These primes don't make any sense to me. What's up? Especially the one on the differential.
I would just have written the same thing without the primes.

I exspect this to be some kind of outdated notation, but it could also be that it just is something I've never seen. Can anyone tell me what's going on?

thx
Frederic

 

[Char. Limit]

I think it's just another way to say $$y(x)=y(0)+i\int f(x) dx$$.

 

[D H]

That x' is just a dummy variable. The only difference between this text and a more modern one is that the more modern text will use greek letters:

$$y(x) = y_0 + i\int_a^x f(\xi)d\xi$$

 

[cristo]

The notation isn't outdated. The integral needs to be a function of x in order to make the equation make sense, and so the upper limit is x. Then, x' is a dummy variable-- this can really be anything you like (apart from x!).

 

[FredericGos]

Thx guys, of course! I get it now. :)