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Differential EquationsEasySystems of Differential Equations

Systems of Differential Equations · Easy problem

The vector functions x1(t)=e2t(11)\mathbf x_1(t)=e^{2t}\begin{pmatrix}1\\1\end{pmatrix} and x2(t)=e−t(1−2)\mathbf x_2(t)=e^{-t}\begin{pmatrix}1\\-2\end{pmatrix} both solve x′=(1120)x\mathbf x'=\begin{pmatrix}1&1\\2&0\end{pmatrix}\mathbf x. Find their Wronskian W(t)=det⁡[x1(t)  x2(t)]W(t)=\det\big[\mathbf x_1(t)\ \ \mathbf x_2(t)\big] at t=ln⁡2t=\ln 2.