dy/dx=ky^(1+c)

Determine the solution that satisfies the initial condition y(0)=y(subzero)

The solution is y(subzero)=(1)/((ckT)^(1/c))

but I can't understand how to find it. ok when i integrate

dy/y^(1+c)=kdt, I get y^(-c)/(-c)=kt+C and I don't know what do from there.