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Exercise

1. Solve the following differential equations.
\begin{displaymath}\begin{array}{ll} (a) \ \left\{\begin{array}{l} x_{1}^{\prime... ...n{array}{c} t^{2}\\ 0\\ 0\\ 0 \end{array}\right) \end{array}\end{displaymath}
2. Solve the differential equation by using the system of differential equation.
\begin{displaymath}\begin{array}{l} \ y^{\prime\prime} + 4y^{\prime} + 3y = t \end{array}\end{displaymath}
3. Solve by elimination.
\begin{displaymath}\begin{array}{ll} (a) \ \left\{\begin{array}{rl} x_{1}^{\prim... ...ime} - 3x_{1} + x_{2} &= 2t - 1 \end{array}\right . \end{array}\end{displaymath}