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

[lap]

The question ask to determine whether y = φ(x) = sqrt ( x - 1 ) is a solution of the differential equation 2yy' = 1.

 

[HallsofIvy]

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?

 

[Mugged]

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.

 

[HallsofIvy]

lap has edited his question and changed it completely. My first response was to a different question.