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Solve this equation

  1. Sep 10, 2014 #1
    1. The problem statement, all variables and given/known data
    Get ##f(t)## from ##Af(t)+Bf(t)^C=Dsin(\omega t)##.


    2. Relevant equations



    3. The attempt at a solution

    Sorry guys, but I have no idea what to do :/
     
  2. jcsd
  3. Sep 10, 2014 #2

    Ray Vickson

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    So you want to solve the equation ##ax + b x^c = r## to get ##x##. You can do it if ##c \in \{ 1/4, 1/3, 1/2, 1, 2, 3, 4 \}## because there are formulas for solving linear, quadratic, cubic and quartic equations. However, in other cases you need to use approximations or numerical methods. Even for ##c \in \{1/4,1/3,3,4 \}## the formulas are lengthy and nasty, but at least they exist.
     
  4. Sep 10, 2014 #3
    The only thing I know about A,B,C and D (and sorry for not mentioning that in the first post) is that they are all ##\mathbb{R}##
     
  5. Sep 10, 2014 #4
    So a general closed form does not exist.
     
  6. Sep 10, 2014 #5
    Ok, Ray Vikcson, is there a proof for that?

    I will try to do it numerically, thanks to both!
     
  7. Sep 10, 2014 #6
    If you meant a proof for that such expression with ##C\in\{5,6,7,\ldots\}## don't have a general closed form then look at the Abel-Ruffini theorem.
     
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