Using eigenvalues and eigenvectors solve system of differential equations:
$$x_1'=x_1+2x_2$$ $$x_2' = 2x_1+x_2$$
And find solution for the initial conditions: $x_1(0) = 1; x_2(0) = -1$
I tried to solve it, but I don't have right results, so I can't check my solution. I would like someone to write how he would solve it and what results would he get.