MAT244--2018F > Term Test 2
TT2A-P3
(1/1)
Victor Ivrii:
(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
$$
\mathbf{x}'=\begin{pmatrix}\hphantom{-}4 & \ 1\\
-3 &0\end{pmatrix}\mathbf{x} +
\begin{pmatrix} \hphantom{-}\frac{4e^{4t}}{e^t+1} \\
-\frac{4e^{4t}}{e^t+1}\end{pmatrix},\qquad
\mathbf{x}(0)=\begin{pmatrix}-1 \\
\hphantom{-}3\end{pmatrix}.
$$
Mallory Schneider:
Part a) and b)
Michael Poon:
I think you could also characterise the phase portrait as a node? (unstable node)
Mallory Schneider:
Part C
Victor Ivrii:
--- Quote from: Michael Poon on November 20, 2018, 12:17:52 PM ---I think you could also characterise the phase portrait as a node? (unstable node)
--- End quote ---
Indeed
Computer generated
Navigation
[0] Message Index
Go to full version