# Differential equations

1. May 20, 2016

### chwala

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. May 20, 2016

### Astik

I think you are trying to say here, dy/du = 2v/u and it's not equal to 2.

3. May 20, 2016

### BvU

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. May 20, 2016

### Ray Vickson

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.

5. May 20, 2016

### chwala

I a m sorry the question was to find the co ordinates of the stationary point for the given function $y= f(x)$

6. May 20, 2016

### BvU

That is the problem statement. What Ray means is: what question do you want your helpers to answer ?

7. May 20, 2016