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

  • #1
I wonder if there is an analytical solution to:

b=a*x - x

with a>0, b>0, x>0, θ>1
 

Answers and Replies

  • #2
Erland
Science Advisor
738
136
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.
 
  • #3
22
1
Analytic with respect to which variable?
 
  • #4
Ssnow
Gold Member
532
156
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 ...
 
  • #5
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11,534
remember that for equation of degree up or equal to 55 there is not a solution given by radicals ...
That just gives two options for θ with an analytic solution.
 
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