By theorem 6.19 we know that the solution is \(y=c1(e^λ1t)u1+...+cn(e^λnt)un\)

wiht λi the eigenvalues of the matrix A and ui, the eigenvalues.

Thus for this case we then obtain the general solution:

\([y1,y2]=y=c1e^t[2,-1]+c2e^3t[3,1]\)

Thus we obtain:

\(y1=2c1e^t+3c2e^3t\)

\(y2=-c1e^t+c2e^3t\)