TITLE: Finding correct sign for a square root in a differentiable equation
QUESTION [0 upvotes]: I have this problem, $\frac{dy}{dx}=\frac{2x}y$, $y(6)=-4$ where the solution $y(x)=\pm\sqrt{2x^2+C}$, $C=-56$, is shown, however I don't understand how the correct sign $y(x)=-\sqrt{2x^2-56}$ is found for the square root. square rooting both sides causes the right side to be plus or minus, and I need to find which one is correct.

REPLY [0 votes]: I think instead of finding y and then putting x=6 and y=-4 is not a right method. You have to direct put values in equation you obtain after integrating.
We have,
8 = 36 + c
c = -24
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