# Matematické Fórum

Nevíte-li si rady s jakýmkoliv matematickým problémem, toto místo je pro vás jako dìlané.

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## #1 30. 06. 2020 16:07

Dacu
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### Systém diferenciálních rovnic

Ahoj všichni,

Najdìte všechna øešení systému diferenciálních rovnic

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

Vše nejlepší,

Dacu

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

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## #2 30. 06. 2020 16:30

Ferdish
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### Re: Systém diferenciálních rovnic

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...

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## #3 30. 06. 2020 16:52

Dacu
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### Re: Systém diferenciálních rovnic

#### 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

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

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## #4 01. 07. 2020 17:15

Dacu
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### Re: Systém diferenciálních rovnic

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

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

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

jarrro
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### Re: Systém diferenciálních rovnic

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.

MATH IS THE BEST!!!

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## #7 02. 07. 2020 16:39

Dacu
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### Re: Systém diferenciálních rovnic

Hello ↑ jarrro:

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

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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## #14 03. 07. 2020 10:18

jelena
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### Re: Systém diferenciálních rovnic

Zdravím, OT debata o národních matematických fórech je oddìlena do samostatného tématu, dle zájmu pokraèujte, prosím, v tématu, nebo si založte vlastní v pøíslušné sekci. Dìkuji.

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## #15 07. 07. 2020 18:10

Dacu
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### Re: Systém diferenciálních rovnic

Hello all,

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

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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## #16 07. 07. 2020 20:11

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### Re: Systém diferenciálních rovnic

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

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

Dacu
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### Re: Systém diferenciálních rovnic

↑ 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

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

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## #18 08. 07. 2020 09:36

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### Re: Systém diferenciálních rovnic

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

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

misaH
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### Re: Systém diferenciálních rovnic

$x = \mp\sqrt 3$

But see what did vlado_bb write.

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## #20 08. 07. 2020 13:14

Dacu
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### Re: Systém diferenciálních rovnic

#### misaH napsal(a):

$x = \mp\sqrt 3$.

Hello,

Thousands of apologies!I corrected!Thank you very, 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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## #21 08. 07. 2020 13:42

Dacu
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### Re: Systém diferenciálních rovnic

↑ 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

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

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## #22 08. 07. 2020 16:18

Bati
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### Re: Systém diferenciálních rovnic

↑ 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 $x=-3$.

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## #23 08. 07. 2020 17:48

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### Re: Systém diferenciálních rovnic

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

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

Dacu
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### Re: Systém diferenciálních rovnic

#### 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

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

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

Dacu
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### Re: Systém diferenciálních rovnic

↑ 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!

Odkaz.

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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