Elimination of Arbitrary Constant

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    Constant Elimination
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Discussion Overview

The discussion revolves around the problem of eliminating an arbitrary constant from the equation \( y = \frac{8a^3}{x^2 + 4a^2} \). Participants are exploring the implications of implicit differentiation and seeking clarification on the process involved in eliminating the constant.

Discussion Character

  • Homework-related, Mathematical reasoning, Technical explanation

Main Points Raised

  • One participant notes that the equation appears to be solved for \( y \) and questions the original problem statement.
  • Another participant explicitly states the task is to eliminate the arbitrary constant from the equation.
  • A participant provides a series of manipulations involving implicit differentiation, leading to a derived equation, but seeks further clarification on the implications of their work.
  • There is a concern raised about whether the arbitrary constant has been successfully eliminated, indicating uncertainty in the process.
  • One participant suggests that they have left some work for others to complete, implying that the solution is not fully resolved.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the elimination of the arbitrary constant, as there are multiple viewpoints regarding the effectiveness of the implicit differentiation and whether the constant has been adequately addressed.

Contextual Notes

There are limitations in the discussion regarding the clarity of the original problem statement and the steps taken in the implicit differentiation process, which remain unresolved.

kayella19
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y= 8a³ / x²+4a²
 
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Re: Any one who can solve this?

Hello and welcome to MHB, kayella19! (Wave)

What you've posted isn't a differential equation...and the equation appears to already be solved for y...what is the entire question as it was given to you?
 
Re: Any one who can solve this?

Eliminate the arbitrary constant.
 
Re: Any one who can solve this?

Anyone pleasee? I need your help with this eliminating arbitrary constant. y= 8a³/ (x²+4a²)
 
Re: Any one who can solve this?

kayella19 said:
Anyone pleasee? I need your help with this eliminating arbitrary constant. y= 8a³/ (x²+4a²)

We are given:

$$y=\frac{8a^3}{x^2+4a^2}$$

This implies:

$$\left(x^2+4a^2\right)y=8a^3$$

Implicit differentiation yields:

$$x^2+4a^2=-\frac{2xy}{y'}$$

Hence:

$$-\frac{2xy}{y'}=\frac{8a^3}{y}$$

This implies:

$$\frac{xy^2}{y'}=-4a^3$$

What does implicit differentiation yield?
 
How is that happen? What does implicit differentiation implies?

- - - Updated - - -

The arbitrary constant is'nt eliminated too.
 
kayella19 said:
...The arbitrary constant is'nt eliminated too.

Yes, I left a little bit of work for you to do to complete the problem. :D
 

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