Is y = sqrt(x-1) a Solution to 2yy' = 1?

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Homework Help Overview

The discussion revolves around determining if the function y = φ(x) = sqrt(x - 1) satisfies the differential equation 2yy' = 1. Participants are exploring the relationship between the function and the equation in the context of differential equations.

Discussion Character

  • Exploratory, Problem interpretation

Approaches and Questions Raised

  • Some participants suggest substituting the function into the differential equation to verify if it holds true. Others express confusion about the problem's wording and question the relevance of certain steps in the process.

Discussion Status

The discussion is ongoing, with participants attempting to clarify the problem and explore different interpretations. There is no explicit consensus on the approach to take, but some guidance on substitution has been offered.

Contextual Notes

One participant notes a potential change in the original question, indicating that the context may have shifted during the discussion.

lap
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The question ask to determine whether y = φ(x) = sqrt ( x - 1 ) is a solution of the differential equation 2yy' = 1.
 
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As far as "determine whether y = φ(x) = sqrt ( x - 1 ) is a solution of the differential equation 2yy' = 1" is concerned, there is no reason to "rewrite the equation". If y= sqrt(x- 1)= (x-1)^(1/2) then y'= (1/2)(x- 1)^(-1/2) so that 2yy'= 2(x- 1)^(1/2)[(1/2)(x- 1)^(-1/2)= what?

As for the rest, I don't see how that has anything to do with the problem. Are you sure you haven't looked up the solution to the wrong question?
 
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Your wording is a bit confusing but if you're trying to determine if y(x) is a solution to your differential equation, all you have to do in plug y(x) into the equation and check if it holds.
 
lap has edited his question and changed it completely. My first response was to a different question.
 

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