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In Problems 7–9, solve the related phase plane differential equation (2), page 263, for the given system.$\frac{\mathbf{d}\mathbf{x}}{\mathbf{d}\mathbf{t}}\mathbf{=}\mathbf{2}\mathit{y}\mathbf{-}\mathit{x}\mathbf{,}\frac{\mathbf{d}\mathbf{y}}{\mathbf{d}\mathbf{t}}\mathbf{=}{\mathit{e}}^{\mathbf{x}}\mathbf{+}\mathit{y}$

In Problems 3 – 18, use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t.

$$\begin{gathered} \mathbf{x}\mathbf{\text{'}}\mathbf{+}\mathbf{y}\mathbf{\text{'}}\mathbf{+}\mathbf{2}\mathbf{x}\mathbf{=}\mathbf{0}\mathbf{,} \\ \mathbf{x}\mathbf{\text{'}}\mathbf{+}\mathbf{y}\mathbf{\text{'}}\mathbf{-}\mathbf{x}\mathbf{-}\mathbf{y}\mathbf{=}\mathbf{sint} \end{gathered}$$

Write the given higher-order equation or system in an equivalent normal form (compare Section\({\bf{5}}{\bf{.3}}\)).

\({\bf{3y''' + 2y' - }}{{\bf{e}}^{\bf{t}}}{\bf{y = 5}}\)