mylp[f_]:=LaplaceTransform[f,t,p];
rce=y''[t]+2y'[t]+3y[t]==u[t];
laplasirce=mylp[rce]/.{LaplaceTransform[y[t],t,p]->Y[p],LaplaceTransform[u[t],t,p]->U[p]};
sol=Solve[laplasirce,Y[p]][[1]]

(0==Denominator[Y[p]/.sol]//Solve)/.p->λ

DSolve[y''[t]+2y'[t]+3y[t]==0,y[t],t]

(Solve[y==(ω-y)*Ps*Pz,y]
/.{Ps->(2/(1-p)),Pz->100})//Simplify

sol=Solve[{2x1*p+x2-x1==u,p*x2-x2+3x1==0},{x1,x2}][[1]]

0==Denominator[x2/.sol]//Solve

rce={x1'[t]==-2x1[t]+x2[t]+u[t],
x2'[t]==-x2[t]-2x1[t]-u[t]
};
mylp[rce]/.{LaplaceTransform[x1[t],t,p]->X1[p],LaplaceTransform[u[t],t,p]->U[p],
LaplaceTransform[x2[t],t,p]->X2[p]
};
sol=Solve[%,{X1[p],X2[p]}]//Simplify

0==Denominator[X1[p]/.sol][[1]]//Solve

(({{-2, 1}, {-2, -1}}))//Eigenvalues