Use Laplace transforms to solve the following initial value problems. Where possible, describe the solution behavior in terms of oscillation and decay.

a. \(y^{\prime \prime}-5 y^{\prime}+6 y=0, y(0)=2, y^{\prime}(0)=0\).

b. \(y^{\prime \prime}-y=t e^{2 t}, y(0)=0, y^{\prime}(0)=1\).

c. \(y^{\prime \prime}+4 y=\delta(t-1), y(0)=3, y^{\prime}(0)=0\).

d. \(y^{\prime \prime}+6 y^{\prime}+18 y=2 H(\pi-t), y(0)=0, y^{\prime}(0)=0\).