Solving a function equation

Discussion in 'Physics & Math' started by Secret, Aug 5, 2014.

  1. Secret Registered Senior Member

    Messages:
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    (NOT A HW QUESTION!)
    Saw this when browsing facebook groups
    View attachment 7253

    It reminds me some diff eqt stuff learnt back in 2nd year
    e.g. [f^2]'=2(f'*f)
    e.g. f'=f f=0 or sum(exp(lx),x)

    From fractional calculus, I also briefly came across a function f such that f(f(g))=g'
    http://en.wikipedia.org/wiki/Fractional_calculus

    so what kind of function, when multiplied to the right of another function, will have the same effect as differentiating it?

    From a thread a year ago (answered by rpenner and soem other math guys), I have learnt some basic techniques in solving a function equation including substitutions, looking for patterns and trial and error

    But for this one I am at lost on how to solve it
    Trying to do a dirct integration by collapsing the f'f part into a product rule give me a nonlinear ODE (just as some other guy has done on the comments) of the form f^2-f'=c, so it does not really help
     

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