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## vlado_bb napsal(a):

↑↑ Dacu:Of course he is wrong, and are not roots of .

Hello,

I made the same mistake and you saw that I corrected it ....Bati had to write ....

It is wrong what Bati says, namely:

"Let Then for all " referring to the functions and ?

## vlado_bb napsal(a):

↑↑ Dacu:Such functions do not exist (see the solution by↑↑ jarrro:).

I repeat:

I think that one solution could be and .

Please kindly prove to me that the above solution is not correct!Thank you very much!

All the best,

Dacu

"Don't worry about your difficulties to math.I assure you that mine are even bigger! ” Albert Einstein

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**↑ Dacu:**The proof by jarrro is very clear. Which part you do not understand?

Your functions can only exist on the set . However, they have not derivatives of this set, so they cannot be the solution of your system. So, there is no solution.

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**↑ Dacu:**

I made an oversight, sorry for that. However, my conclusion remains the same. If , then your system becomes

The first equality is true iff , while second is true iff . So your particular ``solution'' works only at points (which could be achieved by a much simpler function if thats what you want)

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**↑ vlado_bb:**

Functions f,g from #21 are defined (and smooth) everywhere

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**↑ vlado_bb:**

I would say no to that... those functions are defined in R and whether they solve something or not is irrelevant in that regard. But this debate is rather pointless, I just wanted to provide a direct argument which I believe Dacu was asking for. jarrro's answer is completely fine as well, of course

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Hello all,

From the "WolframAlpha" read:

Odkaz

Is it correct what "WolframAlpha" displays? I say yes!

All the best,

Dacu

"Don't worry about your difficulties to math.I assure you that mine are even bigger! ” Albert Einstein

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Hi **↑ Dacu:**

I say resolute NO. Lets find the minimal (un)working example:

I hope that you agree that there exist no functions f solving this equation (as the left side is always >=0, but right side is always <0

But wolfram says:

And it is also obvious what it does wrong: It writes , which is fine, but then it squares both sides of equation to convert it to a ''standard'' form, which however results in a very different ODE then the original one (simply because is not equivalent to etc.)

You should never trust blindly these computational engines. They are written (at least initially) by people and it is very difficult, if not impossible, to write it in a way that it processess **any** mathematically valid input. These tools, however, can be very useful for checking your intuition or your computations. That said, they **can not think for you** (yet).

Still, you may try to report this bug to WA. The desktop version of wolfram produces the same result:

DSolve[Abs[f'[x]] == -1 - x^2, f[x], x]

gives the same output as WA, but with a small warning:*Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information.*

Curiously enough, wolfram gives the right answer to (again, no solution).

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## Bati napsal(a):

Hi

↑ Dacu:

I say resolute NO. Lets find the minimal (un)working example:

I hope that you agree that there exist no functions f solving this equation (as the left side is always >=0, but right side is always <0

But wolfram says:

And it is also obvious what it does wrong: It writes , which is fine, but then it squares both sides of equation to convert it to a ''standard'' form, which however results in a very different ODE then the original one (simply because is not equivalent to etc.)

You should never trust blindly these computational engines. They are written (at least initially) by people and it is very difficult, if not impossible, to write it in a way that it processessanymathematically valid input. These tools, however, can be very useful for checking your intuition or your computations. That said, theycan not think for you(yet).

Still, you may try to report this bug to WA. The desktop version of wolfram produces the same result:

DSolve[Abs[f'[x]] == -1 - x^2, f[x], x]

gives the same output as WA, but with a small warning:Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information.

Curiously enough, wolfram gives the right answer to (again, no solution).

Hello,

I think that for the answer https://www.wolframalpha.com/input/?i=% … 3D-1-x%5E2 is correct , because it considers that , , and ...

All the best,

Dacu

"Don't worry about your difficulties to math.I assure you that mine are even bigger! ” Albert Einstein

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**↑ Dacu:**

Even if this was true, this function cannot be a solution on the whole line (it fails in ). At any case, you **really should** specify this first and then you should also explain what do you mean by a solution (for someone, it may be not enough that the solution works only pathwise). I think your system becomes a usual real ODE system after applying a simple substitution and so there is no reason to assume you haven't applied it already.

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