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MAT244--2018F => MAT244--Tests => Term Test 2 => Topic started by: Victor Ivrii on November 20, 2018, 05:52:12 AM

Title: TT2A-P3
Post by: Victor Ivrii on November 20, 2018, 05:52:12 AM
(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
$$
\mathbf{x}'=\begin{pmatrix}\hphantom{-}4 & \ 1\\
-3 &0\end{pmatrix}\mathbf{x} +
\begin{pmatrix} \hphantom{-}\frac{4e^{4t}}{e^t+1} \\
-\frac{4e^{4t}}{e^t+1}\end{pmatrix},\qquad
\mathbf{x}(0)=\begin{pmatrix}-1 \\
\hphantom{-}3\end{pmatrix}.
$$
Title: Re: TT2A-P3
Post by: Mallory Schneider on November 20, 2018, 12:08:17 PM
Part a) and b)
Title: Re: TT2A-P3
Post by: Michael Poon on November 20, 2018, 12:17:52 PM
I think you could also characterise the phase portrait as a node? (unstable node)
Title: Re: TT2A-P3
Post by: Mallory Schneider on November 20, 2018, 12:27:36 PM
Part C
Title: Re: TT2A-P3
Post by: Victor Ivrii on November 25, 2018, 12:34:25 PM
I think you could also characterise the phase portrait as a node? (unstable node)
Indeed


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