Systems of Differential Equations · Challenge problem

For $t>0$, solve the Cauchy–Euler system $t\,\mathbf x'=\begin{pmatrix}1&2\\2&1\end{pmatrix}\mathbf x$ with $\mathbf x(1)=\begin{pmatrix}1\\0\end{pmatrix}$, and find $x_1(2)$.