Matematické Fórum

Dacu · 30. 06. 2020 16:07

Ahoj všichni,

Najděte všechna řešení systému diferenciálních rovnic

$\begin{cases}|f(x)-3g'(x)|=x^2-3 \\|3g(x)-f'(x)|=3-x^2 \end{cases}$

Vše nejlepší,

Dacu

Ferdish · 30. 06. 2020 16:30

Listen to me, my friend.

It is apparent that your mother tongue is not Czech nor Slovak and your communication via translator does not seem to work very well. Otherwise you would already understand what we were trying to tell you.

It is essential for you to understand how the things work around here. First, it is convenient to read through our forum rules. Unfortunately I have no knowledge about our rules being available in other than Czech language. No wonder - 99% of active members here are Czechs or Slovaks or at least Czech/Slovak fluent speakers so there was no need for variations in other languages. If you want I can translate them for you (much better than the software you use for translation - believe that).

I hope you understand this text, since I am not sure if you speak English at all...

Dacu · 30. 06. 2020 16:52

Ferdish napsal(a):
Listen to me, my friend.

It is apparent that your mother tongue is not Czech nor Slovak and your communication via translator does not seem to work very well. Otherwise you would already understand what we were trying to tell you.

It is essential for you to understand how the things work around here. First, it is convenient to read through our forum rules. Unfortunately I have no knowledge about our rules being available in other than Czech language. No wonder - 99% of active members here are Czechs or Slovaks or at least Czech/Slovak fluent speakers so there was no need for variations in other languages. If you want I can translate them for you (much better than the software you use for translation - believe that).

I hope you understand this text, since I am not sure if you speak English at all...

I understood!I'm very sorry to bother you, but I want to understand math as well as possible ... Thank you very much for your understanding!

All the best,

Dacu

Dacu · 01. 07. 2020 17:15

Hello all,

No one is answering?The proposed problem may seem strange, but I think it has a simple solution, because it requires solving a system of differential equations with modules ...

All the best,

Dacu

jarrro · 02. 07. 2020 06:56 — Editoval jarrro (02. 07. 2020 06:56)

since $x^2-3=-$3-x^2$$ the given system can be satisfied if and only if $x^2-3=0$ which satisfy only two numbers x.
Diffferential equation and their systems should be satisfied on some nondegenerated opn interval. So this system cannot be satisfied.
I hope I dont male a mistake.

Dacu · 02. 07. 2020 16:39

Hello ↑ jarrro:

I think we should start from the definition of the module ...

All the best,

Dacu

jelena · 03. 07. 2020 10:18

Zdravím, OT debata o národních matematických fórech je oddělena do samostatného tématu, dle zájmu pokračujte, prosím, v tématu, nebo si založte vlastní v příslušné sekci. Děkuji.

Dacu · 07. 07. 2020 18:10

Hello all,

I think we should start from the definition of the module ...

All the best,

Dacu

vlado_bb · 07. 07. 2020 20:11

↑ Dacu: Why? The problem has been solved by ↑ jarrro:

Dacu · 08. 07. 2020 09:30 — Editoval Dacu (08. 07. 2020 13:44)

vlado_bb napsal(a):
↑ Dacu: Why? The problem has been solved by ↑ jarrro:

Hello,

From $x ^ 2-3 = 0$ results $x = \mp \sqrt{3}$ and so what are the values of the functions $f (x)$ and $g (x)$ for $x = \mp \sqrt{3}$ ?
Thank you very much!

All the best,

Dacu

vlado_bb · 08. 07. 2020 09:36

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

misaH · 08. 07. 2020 11:02 — Editoval misaH (08. 07. 2020 11:03)

$x = \mp\sqrt 3$

But see what did vlado_bb write.

Dacu · 08. 07. 2020 13:14

misaH napsal(a):
$x = \mp\sqrt 3$ .

Hello,

Thousands of apologies!I corrected!Thank you very, very much!

All the best,

Dacu

Dacu · 08. 07. 2020 13:42

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

I think that one solution could be $f(x) = \frac{1}{2} c_1 e^{-x} (e^{2 x} + 1) + \frac{3}{2} c_2 e^{-x} (e^{2 x} - 1) + x^2 + 2 x - 1$ and $g(x) = \frac{1}{6} c_1 e^{-x} (e^{2 x} - 1) + \frac{1}{2} c_2 e^{-x} (e^{2 x} + 1) + \frac{1}{3} (x^2 + 2 x - 1)$ .
Please kindly prove to me that the above solution is not correct!Thank you very much!

All the best,

Dacu

Bati · 08. 07. 2020 16:18

↑ Dacu:
Let $c_1=c_2=0$ . Then $f(x)-3g'(x)=0$ for all $x\in\mathbb{R}$ , but $x^2-3=0$ only if $x=3$ or $x=-3$ .

vlado_bb · 08. 07. 2020 17:48

↑ Dacu:The proof that your solution is wrong has already been done by ↑ jarrro:. Don't you understand his proof?

Dacu · 10. 07. 2020 06:07 — Editoval Dacu (10. 07. 2020 06:18)

Bati napsal(a):
↑ Dacu:
Let $c_1=c_2=0$ . Then $f(x)-3g'(x)=0$ for all $x\in\mathbb{R}$ , but $x^2-3=0$ only if $x=3$ or $x=-3$ .

Hello,

I think you meant that $x=\mp \sqrt{3}$ ...What other values can $c_1$ and $c_2$ take and so what are all the solutions of nonlinear system of the differential equations?Thank you very much!

All the best,

Dacu

Dacu · 10. 07. 2020 06:15 — Editoval Dacu (10. 07. 2020 06:18)

vlado_bb napsal(a):
↑ Dacu:The proof that your solution is wrong has already been done by ↑ jarrro:. Don't you understand his proof?

Hello,

Bati has a different opinion ... Is it wrong what Bati says?!?!Thank you very much!

From the "WolframAlpha" reading:

Odkaz.

All the best,

Dacu

Matematické Fórum

#1 30. 06. 2020 16:07

Systém diferenciálních rovnic

#2 30. 06. 2020 16:30

Re: Systém diferenciálních rovnic

#3 30. 06. 2020 16:52

Re: Systém diferenciálních rovnic

Ferdish napsal(a):

#4 01. 07. 2020 17:15

Re: Systém diferenciálních rovnic

#5 02. 07. 2020 06:56 — Editoval jarrro (02. 07. 2020 06:56)

Re: Systém diferenciálních rovnic

#6 02. 07. 2020 13:46 — Editoval krakonoš (02. 07. 2020 13:55) Příspěvek uživatele krakonoš byl skryt uživatelem jelena. Důvod: OT, viz samostatné téma

#7 02. 07. 2020 16:39

Re: Systém diferenciálních rovnic

#8 02. 07. 2020 16:59 — Editoval vanok (02. 07. 2020 17:00) Příspěvek uživatele vanok byl skryt uživatelem jelena. Důvod: OT, viz samostatné téma

#9 02. 07. 2020 17:52 — Editoval krakonoš (02. 07. 2020 17:52) Příspěvek uživatele krakonoš byl skryt uživatelem jelena. Důvod: OT, viz samostatné téma

#10 02. 07. 2020 22:58 — Editoval vanok (02. 07. 2020 23:01) Příspěvek uživatele vanok byl skryt uživatelem jelena. Důvod: OT, viz samostatné téma

#11 02. 07. 2020 23:27 — Editoval misaH (02. 07. 2020 23:29) Příspěvek uživatele misaH byl skryt uživatelem jelena. Důvod: OT, viz samostatné téma

#12 02. 07. 2020 23:43 Příspěvek uživatele Ferdish byl skryt uživatelem jelena. Důvod: OT, viz samostatné téma

#13 03. 07. 2020 07:37 — Editoval krakonoš (03. 07. 2020 07:38) Příspěvek uživatele krakonoš byl skryt uživatelem jelena. Důvod: OT, viz samostatné téma

#14 03. 07. 2020 10:18

Re: Systém diferenciálních rovnic

#15 07. 07. 2020 18:10

Re: Systém diferenciálních rovnic

#16 07. 07. 2020 20:11

Re: Systém diferenciálních rovnic

#17 08. 07. 2020 09:30 — Editoval Dacu (08. 07. 2020 13:44)

Re: Systém diferenciálních rovnic

vlado_bb napsal(a):

#18 08. 07. 2020 09:36

Re: Systém diferenciálních rovnic

#19 08. 07. 2020 11:02 — Editoval misaH (08. 07. 2020 11:03)

Re: Systém diferenciálních rovnic

#20 08. 07. 2020 13:14

Re: Systém diferenciálních rovnic

misaH napsal(a):

#21 08. 07. 2020 13:42

Re: Systém diferenciálních rovnic

vlado_bb napsal(a):

#22 08. 07. 2020 16:18

Re: Systém diferenciálních rovnic

#23 08. 07. 2020 17:48

Re: Systém diferenciálních rovnic

#24 10. 07. 2020 06:07 — Editoval Dacu (10. 07. 2020 06:18)

Re: Systém diferenciálních rovnic

Bati napsal(a):

#25 10. 07. 2020 06:15 — Editoval Dacu (10. 07. 2020 06:18)

Re: Systém diferenciálních rovnic

vlado_bb napsal(a):

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