change of variables question in 1st order proof

in differential equations when solving an initial value problem for c, you have this proof in Braun where he changes f(t) to f(r), g(t) to g(s)- I'm not sure what the reasoning is, maybe you can use any arbitrary variable? the time dependence of y on t also remains?

Re: change of variables question in 1st order proof

Hey mathlover10.

They are just dummy variables: my guess is that he is trying to avoid using the variables t, t0, y and y0 for the limits.

Remember that Integral 0 to x f(x)dx is a lot more complicated than Integral 0 to x f(s)ds. The second one is usually what is meant but sometimes you can get situations resembling the first (The Fresnel integrals come to mind).