Let $A(t) = \left[\begin{array}{l}2t&0&1\\0&2t&1\\0&-1&2t\end{array}\right]$ be the matrix of $\dot x = A(t) x $. The question is to obtain the resolvent matrix.

I did: $\dot x - \dot y = 2t(x-y) \implies x - y=0 // x-y=e^{t^2 }$ ... but when i substitute this on the third ecuation i don't know where to follow. Any hint is greatly appreciated, thank you.