For a separable differential eqn, when you integrate both sides and one has a negative, does the C value depend on which side the - is on?
If I understand your question correctly then no it shouldn't depend on which side the minus sign is on. Once you find the value of C by applying the initial condition and get the solution in the form "y(x) = " it should be exactly the same solution.
MD is correct. Your value of C may change depending on which side of the equation it's on, but your y(x) will not change.