\left. \begin{gathered}
 y = C_1 e^{ix} + C_2 e^{ - ix} \Rightarrow C_1 + C_2 = y_0 \hfill \\
 y' = iC_1 e^{ix} - iC_2 e^{ - ix} \Rightarrow C_1 - C_2 = - iy_1 \hfill \\ 
\end{gathered} \right\} \Rightarrow C_1 = \frac{{y_0 - iy_1 }}
{2},C_2 = \frac{{y_0 + iy_1 }}
{2}