Find all positive differentiable functions \(f\) that satisfy\(\int_0^x \sin(t) f(t) dt = [f(x)]^2-1\)for all real numbers \(x\).
I am very new to integration and I have no idea how to approach this problem. Help will be greatly apreciated!!!
I have been playing with this but I cannot quite get it to work.
I do not really know what I am doing.
If Alan or Heureka or some other talented mathematician could show us both that would be great.
