OK, that was too easy, as there was an exact symbolic solution.

Is this a solution Sage could have given symbolically as well? 

Here are the results for sin(1/x)==x on [-1,1] :

It apparently computed many solutions and originally asked me whether I 
wanted to show all the found solutions or just some of them, and I pressed 
show all. It also tells you that it "couldn't prove that these are all of 
the solutions." There are many more solutions given however these are all I 
could fit on the screen. 


On Thursday, March 15, 2018 at 5:56:54 PM UTC-5, Dima Pasechnik wrote:
>
>
>
> On Thursday, March 15, 2018 at 10:23:44 PM UTC, saad khalid wrote:
>>
>> I have to apologize, I gave a slightly incorrect Mathematica code 
>> earlier, the actual code was:
>>
>> Solve[ Exp[-2*a*x]-1+4*a*x==0,x]//N
>>
>> The earlier code gave the wrong answer. Anyways:
>>
>> it could be a different function, which potentially would run much 
>>> longer, by repetitive splitting of the interval
>>> (I guess that's what Mathematica is doing)  
>>>
>>
>> There appear to be 2 main solving functions in Mathematica, "Solve" and 
>> "Reduce," the differences are explained in this well written answer:
>>
>> https://mathematica.stackexchange.com/questions/17127/what-is-the-difference-between-reduce-and-solve
>>
>> What is the result of such a Mathematica command on an example with 
>>> infinitely many roots given in this thread?
>>
>>
>>
>> So, the Solve function doesn't find any it seems but it tells you to use 
>> the Reduce function, which I think does give all the solutions. 
>>
>
> OK, that was too easy, as there was an exact symbolic solution.
> How about solving sin(1/x)==x on [-1,1] instead?
>  
>

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