Differential equations

  • Thread starter chwala
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  • #1
chwala
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Homework Statement


Get the two stationary points for the equation ## y= ((ln x)^2)/x ##

Homework Equations




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##
 
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  • #2
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therefore
dy/dx=2u/u=2dy/dx=2u/u=2dy/dx=2u/u = 2 is this correct?
I think you are trying to say here, dy/du = 2v/u and it's not equal to 2.
 
  • #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 ?
 
  • #4
Ray Vickson
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Homework Statement


Get the two stationary points for the equation ## y= ((ln x)^2)/x ##

Homework Equations




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##
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.
 
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  • #5
chwala
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I a m sorry the question was to find the co ordinates of the stationary point for the given function ## y= f(x)##
 
  • #6
BvU
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That is the problem statement. What Ray means is: what question do you want your helpers to answer ?
 
  • #7
chwala
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I have answered the question already sorry
 

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