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Question Number 2130 by Yozzi last updated on 03/Nov/15

Find r= (((x(t))),((y(t))) )   satisfying                            (dr/dt)+Ar=0  where A= [((−3    −1)),((8          3)) ] by using  a matrix integrating factor.

$${Find}\:\boldsymbol{{r}}=\begin{pmatrix}{{x}\left({t}\right)}\\{{y}\left({t}\right)}\end{pmatrix}\:\:\:{satisfying}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{d}\boldsymbol{{r}}}{{dt}}+\boldsymbol{{Ar}}=\mathrm{0} \\ $$$${where}\:\boldsymbol{{A}}=\begin{bmatrix}{−\mathrm{3}\:\:\:\:−\mathrm{1}}\\{\mathrm{8}\:\:\:\:\:\:\:\:\:\:\mathrm{3}}\end{bmatrix}\:{by}\:{using} \\ $$$${a}\:{matrix}\:{integrating}\:{factor}. \\ $$

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