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Find a Few Functions (Posted on 2018-04-15) Difficulty: 3 of 5
Find solutions for f(x) and g(x), such that:

(1): {f(x) + f'(x)}^2 = 1 + f(2x)

(2): {g(x) + g'(x)}^2 = 2*(g(x) + g(2x))

No Solution Yet Submitted by Larry    
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Sorry, I goofed on Part (2) | Comment 2 of 3 |
My apologies.
I was thinking e^x for g(x) as Charlie was surmising, but I totally blew it.   My mistake.

And f(x) = sin(x) is also what I had in mind for part (1), though I don't know whether this is a unique solution or not.
  Posted by Larry on 2018-04-15 18:20:01
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