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Differential equations

  1. May 20, 2016 #1
    1. The problem statement, all variables and given/known data
    Get the two stationary points for the equation ## y= ((ln x)^2)/x ##

    2. Relevant equations


    3. The attempt at a solution
    i have managed to solve
    ##dy/dx=((2xlnx/x- (ln x)^2))/x^2 = 0,
    ln x(2-ln x) = 0,
    x= 1, x =e^2##
     
    Last edited: May 20, 2016
  2. jcsd
  3. May 20, 2016 #2
    I think you are trying to say here, dy/du = 2v/u and it's not equal to 2.
     
  4. May 20, 2016 #3

    BvU

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    I can follow $$
    { dy\over dx} ={2x\ln x/x- (ln x)^2)\over x^2} = 0 \ \ \Leftrightarrow\ \ \ln x(2-ln x) = 0 \ \ \& \ \ x\ne 0 $$
    which is satisfied for ##x= 1## and for ##x =e^2##.
    But the 'then I am getting' seems a bit superfluous to me. What do you intend to show with that ?
     
  5. May 20, 2016 #4

    Ray Vickson

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    So, what is your question?

    Anyway, please use proper syntax for TeX/LaTex: you should type "\ln ..." instead of "ln ...", because leaving out the backslash produces ugly results that are hard to read, like this (##ln x##) while using "\ln..." produces good-looking, easier-to-read results, like this (##\ln x##). BTW: the same goes for sin/arcsin, cos/arccos, tan/arctan, exp, log, max, min, lim, sinh, cosh, tanh, etc: leaving out the backslash gives ugly, hard-to-read results ##sin x##, ##arcsin x##, ##cos x##, ##arccos x##, ##tan x##, ##arctan x##, ##exp x##, ##log x##, ##max x##, ##min x##, ##lim_{x \to 0}##, ##sinh x##, etc., etc. Using the backslash produces much nicer output: ##\sin x##, ##\arcsin x##, ##\cos x##, ##\arccos x##, ##\tan x##, ##\arctan x##, ##\exp x##, ##\log x##, ##\max x##, ##\min x##, ##\lim_{x \to 0}##, ##\sinh x##, etc.
     
  6. May 20, 2016 #5
    I a m sorry the question was to find the co ordinates of the stationary point for the given function ## y= f(x)##
     
  7. May 20, 2016 #6

    BvU

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    That is the problem statement. What Ray means is: what question do you want your helpers to answer ?
     
  8. May 20, 2016 #7
    I have answered the question already sorry
     
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