8.1.2.68 Second order differential equations

condition: Find a general solution to a second-order differential equation and a particular solution that satisfies the given initial conditions \( \left(x_{0}, y_{0}, y_{0}^{\prime}\right) \). \[ y^{\prime \prime}-5 y^{\prime}+6 y=2 \cos x, y_{0}=3, y_{0}^{\prime}=\frac{1}{2}, x_{0}=0 \]