In 18, the general solution of the linear system X AX is given
Chapter 11, Problem 4(choose chapter or problem)
In Problems 1–8, the general solution of the linear system \(\mathbf X^\prime=\mathbf{AX}\)is given.
(a) In each case discuss the nature of the solution in a neighborhood of (0, 0).
(b) With the aid of a graphing utility plot the solution that satisfies X(0) = (1, 1).
\(\mathbf{A}=\left(\begin{array}{rr}-1 & -4 \\ 1 & -1\end{array}\right), \quad \mathbf{X}(t)=e^{-t}\left[c_{1}\left(\begin{array}{c} 2 \cos 2 t \\ \sin 2 t \end{array}\right)+c_{2}\left(\begin{array}{c} -2 \sin 2 t \\ \cos 2 t \end{array}\right)\right]\)
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