For each of the following, determine a differential equation (or a system of Dif EQ's), which has the expression of what is below for the general sol'n.

1.) $\displaystyle y=c_1\cos(\sqrt{2}t)+c_2\sin(\sqrt{2}t)$

2.) $\displaystyle y=c_1e^{4t}+c_2te^{4t}$

3.) $\displaystyle \textbf{X}=c_1\left(\begin{array}{r}0\\1 \end{array}\right)e^{-3t}+c_2\left(\begin{array}{r} 1\\0 \end{array}\right)e^{2t}$