1. The problem statement, all variables and given/known data Hello. I want to study the stability of the origin of the following problem: dx/dt = -2y dy/dt = x + 2y dz/dt = -2z So the eigenvalues of this 3 x 3 matrix are -2, 1 + i, 1-i. The eigenvectors are (0,0,1) , (2,-1-i,0), (-2,-1+i,0). The solution (confirmed with Mathematica) is given by: x(t) = 2*exp(t)cos(t) * C_1 + 2*exp(t)*sin(t) * C_2 - 2*exp(t)*sin(t) *C_3 y(t) = C_1 * (-exp(t)*¨sin(t) - exp(t)*cos(t)) + C_2 * (exp(t)cos(t) -exp(t)sin(t)) + C_3 * (-exp(t)cos(t)+exp(t)sin(t) ) z(t) = 2*exp(2*t) *C_3 Where C_1,C_2,C_3 are constants. How can I find (analytically, not by plotting) if the origin (0,0,0) is stable, asymptotically stable? unstable, a node, a center? I'm having trouble figuring this out. Can you please help?