MHB Elimination of Arbitrary Constant

[kayella19]

y= 8a³ / x²+4a²

 

[MarkFL]

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?

 

[kayella19]

Re: Any one who can solve this?

Eliminate the arbitrary constant.

 

[kayella19]

Re: Any one who can solve this?

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

 

[MarkFL]

Re: Any one who can solve this?

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?

 

[kayella19]

How is that happen? What does implicit differentiation implies?

- - - Updated - - -

The arbitrary constant is'nt eliminated too.

 

[MarkFL]

...The arbitrary constant is'nt eliminated too.

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