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**MAT244 Math--Lectures / Phase portraits - Improper nodes**

« **on:**November 19, 2014, 11:02:48 AM »

Prof, how about direction of improper node?

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Prof, how about direction of improper node?

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Q2: 7.6 #6

r^{2}+9=0

r_{1}=3i, r2=-3i

pure imaginary eigenvalue, so it's stable center

also whole soln is in the q1 fisrt post.

r

r

pure imaginary eigenvalue, so it's stable center

also whole soln is in the q1 fisrt post.

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Draw a full phase portrait and describe completely the type of the stationary point indicating if it is stable or unstable and in the case of the center and focus indicate orientation (clockwise or counter-clockwise)

\begin{equation*}

\textbf{x}'=\begin{pmatrix}

-2 & \hphantom{-}1\\ \hphantom{-}1 &-2

\end{pmatrix}\textbf{x}\ .

\end{equation*}

sorry two picture can't see normally, there are two links of picture of q1 and q2

http://www.imagebam.com/image/f84041363999992

http://www.imagebam.com/image/64d11b364003377

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