No solution for an arbitrary constant.

Say I have found a general solution to an equation of motion, which is, simple harmonic motion.

The general solution I have found is of the form:

When inserting some (supplied) inital conditions, I am able to solve to find but cannot find a solution for , does it follow that ?

My initial conditions contain only the position when , and no derivatives of it - this being the case

I hope it does, because I'm stumped if not - If the question above is too vague, I can supply the full question. However, I want to solve it myself and this is why I have used generic formulae above.