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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!!!

 Aug 22, 2021
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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.

 Aug 22, 2021

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