Toronto Math Forum
MAT244--2018F => MAT244--Tests => Term Test 2 => Topic started by: Victor Ivrii on November 20, 2018, 05:52:12 AM
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(a) Find the general solution of
$$
\mathbf{x}'=\begin{pmatrix} \ 4 & \ 1\\
-3 &0\end{pmatrix}\mathbf{x}.$$
(b) Sketch corresponding trajectories. Describe the picture (stable/unstable, node, focus, center, saddle).
(c) Solve
$$
\mathbf{x}'=\begin{pmatrix}\hphantom{-}4 & \ 1\\
-3 &0\end{pmatrix}\mathbf{x} +
\begin{pmatrix} \hphantom{-}\frac{4e^{4t}}{e^t+1} \\
-\frac{4e^{4t}}{e^t+1}\end{pmatrix},\qquad
\mathbf{x}(0)=\begin{pmatrix}-1 \\
\hphantom{-}3\end{pmatrix}.
$$
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Part a) and b)
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I think you could also characterise the phase portrait as a node? (unstable node)
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Part C
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I think you could also characterise the phase portrait as a node? (unstable node)
Indeed
Computer generated