In Problems 1–7, convert the given initial value problem into an initial value problem for a system in normal form.

$$\begin{gathered} \mathbf{x}\mathbf{\text{'}}\mathbf{\text{'}}\mathbf{+}\mathbf{y}\mathbf{-}\mathbf{x}\mathbf{\text{'}}\mathbf{=}\mathbf{2}\mathbf{t}\mathbf{;}\mathbf{x}\mathbf{\left(}\mathbf{3}\mathbf{\right)}\mathbf{=}\mathbf{5}\mathbf{,}\mathbf{x}\mathbf{\text{'}}\mathbf{\left(}\mathbf{3}\mathbf{\right)}\mathbf{=}\mathbf{2}\mathbf{,} \\ \mathbf{y}\mathbf{\text{'}}\mathbf{\text{'}}\mathbf{-}\mathbf{x}\mathbf{+}\mathbf{y}\mathbf{=}\mathbf{-}\mathbf{1}\mathbf{;}\mathbf{y}\mathbf{\left(}\mathbf{3}\mathbf{\right)}\mathbf{=}\mathbf{1}\mathbf{,}\mathbf{y}\mathbf{\text{'}}\mathbf{\left(}\mathbf{3}\mathbf{\right)}\mathbf{=}\mathbf{-}\mathbf{1} \end{gathered}$$

[hint]${\mathbf{x}}_{\mathbf{1}}\mathbf{=}\mathbf{x}\mathbf{,}{\mathbf{x}}_{\mathbf{2}}\mathbf{=}\mathbf{x}\mathbf{\text{'}}\mathbf{,}{\mathbf{x}}_{\mathbf{3}}\mathbf{=}\mathbf{y}\mathbf{,}{\mathbf{x}}_{\mathbf{4}}\mathbf{=}\mathbf{y}\mathbf{\text{'}}$

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