\text { Suppose }\left[\begin{array}{l} y_{1}(t) \\ y_{2}(t) \end{array}\right] \text { solves the following system of first-order linear ODEs: } \left[\begin{array}{l} y_{1}^{\prime}(t) \\ y_{2}^{\prime}(t) \end{array}\right]=\left[\begin{array}{cc} 0 & 1 \\ -2 & -2 \end{array}\right]\left[\begin{array}{l} y_{1}(t) \\ y_{2}(t) \end{array}\right]+\left[\begin{array}{c} 0 \\ e^{-t} \cos (t) \end{array}\right] (a) (1 point) Find constants b, c and a function f(t), such that y₁ (t) solves the secon-dorder linear ODE y_{1}^{\prime \prime}(t)+b y_{1}^{\prime}(t)+c y_{1}(t)=f(t) (b) (2 points) For the second-order linear ODE that you wrote down in part (a), find aparticular solution.

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