For which variable do you want to solve this equation? 

All of the following work: sgn(sqrt(3.)), sgn(3.^(1/2)), sgn(4), sgn(4.), sgn(sqrt(`3`)), sgn(sqrt(`3^(1./2)`) in Maple 2016. But not sgn(3^(1/2)).

@Mariusz Iwaniuk And there are 3 parameters (alpha, k and _C1)

Please do not shout (writing in all caps) at us. Also, how is your problem related to Maple?

How is this question related to Maple? 

Is this a Maple question or a general math question? If it is the latter, perhaps you should ask your question elsewhere, for example at stackexchange: https://math.stackexchange.com/.