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Differential EquationsEasySystems of Differential Equations

Systems of Differential Equations · Easy problem

The system x′=(−114−1)x\mathbf x'=\begin{pmatrix}-1&1\\4&-1\end{pmatrix}\mathbf x has general solution x(t)=c1et(12)+c2e−3t(1−2)\mathbf x(t)=c_1e^{t}\begin{pmatrix}1\\2\end{pmatrix}+c_2e^{-3t}\begin{pmatrix}1\\-2\end{pmatrix}. For the solution with x(0)=(20)\mathbf x(0)=\begin{pmatrix}2\\0\end{pmatrix}, find x1(ln⁡2)x_1(\ln 2).