Elimination of Arbitrary Constant

In summary, the equation y= 8a³ / (x²+4a²) can be simplified by eliminating the arbitrary constant using implicit differentiation, which yields the equation xy^2 / y' = -4a^3.
  • #1
kayella19
8
0
y= 8a³ / x²+4a²
 
Physics news on Phys.org
  • #2
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?
 
  • #3
Re: Any one who can solve this?

Eliminate the arbitrary constant.
 
  • #4
Re: Any one who can solve this?

Anyone pleasee? I need your help with this eliminating arbitrary constant. y= 8a³/ (x²+4a²)
 
  • #5
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:

\(\displaystyle y=\frac{8a^3}{x^2+4a^2}\)

This implies:

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

Implicit differentiation yields:

\(\displaystyle x^2+4a^2=-\frac{2xy}{y'}\)

Hence:

\(\displaystyle -\frac{2xy}{y'}=\frac{8a^3}{y}\)

This implies:

\(\displaystyle \frac{xy^2}{y'}=-4a^3\)

What does implicit differentiation yield?
 
  • #6
How is that happen? What does implicit differentiation implies?

- - - Updated - - -

The arbitrary constant is'nt eliminated too.
 
  • #7
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
 

FAQ: Elimination of Arbitrary Constant

What is the "Elimination of Arbitrary Constant"?

The Elimination of Arbitrary Constant is a mathematical process used to solve equations and systems of equations. It involves removing any arbitrary constants, also known as free parameters, from an equation or system in order to find a unique solution.

When is the Elimination of Arbitrary Constant used?

This process is commonly used in calculus, differential equations, and other areas of mathematics where equations with arbitrary constants need to be solved for specific values.

How does the Elimination of Arbitrary Constant work?

The process typically involves manipulating the equation or system of equations using algebraic operations such as addition, subtraction, multiplication, and division. The goal is to eliminate the arbitrary constant and solve for the remaining variables.

What are some common techniques used in the Elimination of Arbitrary Constant?

Some common techniques include substitution, elimination, and setting up a system of equations. These techniques may vary depending on the complexity of the equation or system being solved.

Are there any limitations to the Elimination of Arbitrary Constant?

Yes, the Elimination of Arbitrary Constant may not always be possible or may lead to complex solutions. It is important to carefully analyze the equation or system before attempting to eliminate the arbitrary constant.

Similar threads

MHB Elimination of arbitrary constants 2
Replies
7
Views
6K
MHB Elimination of arbitrary constants.
Replies
8
Views
4K
I Solving a system of differential equations by elimination
Replies
4
Views
2K
MHB Eliminating constants in a second derivative of a function
Replies
4
Views
3K
MHB Existence of Unique Solution for Nonlinear System with Arbitrary Constants
Replies
1
Views
1K
Chemistry Elimination question on alkyl halide
Replies
0
Views
767
Gauss-Jordan Elimination algorithm steps
Replies
1
Views
806
B Where is the best place to put the arbitrary constant?
Replies
2
Views
1K
Value of "a" between two real roots of quadratic equation
Replies
2
Views
1K
Gaussian Elimination of Singular Matrix with partial pivoting
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top