Note y = 0 is an equiilbrium solution so y is always positive or always negative if y(0) isn't zero.
Without an initial condition I can't see why either to necessarily take the pos sqrt.
eg if y(0) =-1 then y = -cos(x)/(4x+c)
-1 = -1/(c) so c = 1
y = -cos(x)/(4x+1) would be a solution