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Rearrange equation (solution of ODE)

  1. Oct 10, 2014 #1
    I have determined the solution to a nonlinear first order ordinary differential equation but am struggling to rearrange the result, I have that

    $$\\ln(R)+\frac{mR^{n-1}}{n-1}=\bar{w}_{\infty}\xi+C.$$

    How would I rearrange this equation for $$R$$?
     
    Last edited: Oct 10, 2014
  2. jcsd
  3. Oct 10, 2014 #2

    Stephen Tashi

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    Science Advisor

    Do you mean that [itex] R(x) [/itex] is the function that solves a differential equation in the variable [itex] x [/itex] ?
     
  4. Oct 10, 2014 #3

    pasmith

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    Homework Helper

    You can't. What you have is essentially [tex]
    \ln(R^{n-1}) + mR^{n-1} = A[/tex] which doesn't have an analytic solution for [itex]R^{n-1}[/itex] given [itex]A[/itex].
     
  5. Oct 10, 2014 #4
    Sorry I should have been more clear. I have determined the solution [itex] R(\xi) [/itex], the solution is

    $$\ln(R(\xi))+\frac{mR(\xi)^{n-1}}{n-1}=\bar{w}_{\infty}\xi+C.$$

    I simply need to rearrange this to say [itex] R(\xi)=\cdots [/itex]
     
  6. Oct 10, 2014 #5

    HallsofIvy

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    That was clear. And what you have been told that there is no solution in terms of elementary functions.
     
  7. Oct 10, 2014 #6

    Mark44

    Staff: Mentor

    The question has been asked and answered, so I'm closing this thread.
     
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