Solving the Equation (y^2)+(y')^2=1: Ideas and Guidance

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Homework Help Overview

The problem involves finding a function \( y \) such that the sum of its square and the square of its derivative equals one, represented by the equation \( (y^2) + (y')^2 = 1 \). This falls within the context of differential equations and potentially trigonometric identities.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between the function and its derivative, with one suggesting the use of trigonometric identities. Others express confusion about how the derivative is involved in the equation.

Discussion Status

Some guidance has been offered, including the suggestion to consider trigonometric identities and the possibility of integrating a derived expression. However, there is still uncertainty among participants regarding the approach to take.

Contextual Notes

Participants are grappling with the interpretation of the problem and the role of the derivative in the context of the given equation. There is an indication that guessing a solution might be a valid strategy, but this has not been universally accepted.

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Homework Statement



Find a function of y whose square plus the square of its derivative is 1.
i.e. (y^2)+(y')^2=1 and carry out your ideas.


Homework Equations





The Attempt at a Solution



Can anyone just help me out with this one. Kinda confused by the questioning. Just point me in the right direction.
 
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Think trig identities...
 
I still don't see it. How does the derivative factor into it?
 
Dr. Lady is suggesting you simply guess the answer.
Otherwise you have y'=+/-sqrt(1-y^2). You can try to integrate that.
 

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