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I Analytical solution to b=a*x^-theta - x?

  1. Jun 3, 2016 #1
    I wonder if there is an analytical solution to:

    b=a*x - x

    with a>0, b>0, x>0, θ>1
     
  2. jcsd
  3. Jun 3, 2016 #2

    Erland

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    Science Advisor

    Do you by "analytical solution" mean a function built up from elementary functions? If so, the answer is almost certainly no, but I can't prove it.
     
  4. Jun 3, 2016 #3
    Analytic with respect to which variable?
     
  5. Jun 5, 2016 #4

    Ssnow

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    Do you want to search for ##x=\sum_{i=0}^{\infty}a_{i}y^{i}##? In this case put ##x## in ##bx^{\theta}=a-x^{\theta+1}## and try to solve a system (infinite) involving equations with the coefficients ##a_{i}##. If you want simply the solutions of ##bx^{\theta}-a+x^{\theta+1}=0##, you must start to consider different value of ##\theta##, remember that for equation of degree up or equal to ##5## there is not a solution given by radicals ...
     
  6. Jun 5, 2016 #5

    mfb

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    Staff: Mentor

    That just gives two options for θ with an analytic solution.
     
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