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.](https://www.tinkutara.com/question/Q2130.png)
$${Find}\:\boldsymbol{{r}}=\begin{pmatrix}{{x}\left({t}\right)}\\{{y}\left({t}\right)}\end{pmatrix}\:\:\:{satisfying}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{d}\boldsymbol{{r}}}{{dt}}+\boldsymbol{{Ar}}=\mathrm{0} \\ $$$${where}\:\boldsymbol{{A}}=\begin{bmatrix}{−\mathrm{3}\:\:\:\:−\mathrm{1}}\\{\mathrm{8}\:\:\:\:\:\:\:\:\:\:\mathrm{3}}\end{bmatrix}\:{by}\:{using} \\ $$$${a}\:{matrix}\:{integrating}\:{factor}. \\ $$