Characteristic polynomial and Eigenvalues functions are not giving any result why?
Tenenbaum p. 291 shows this is correct. Suppose X'=AX+B where A is the matrix. A={{-p,q},{b,-q}} B={r,s}. dx/dt=ay-px+r, dy/dt=bx-qy+s. X[t]={x[t],y[t]}, X[0]=[x0,y0]
In[378]:=
CharacteristicPolynomial[{{-p, a}, {b, -q}}, m] ==
Det[{{-p, a}, {b, -q}} - m {{1, 0}, {0, 1}}]
Out[378]= True
You should explain the problem more and even why you move between each step (ex, what book and chapter you are in - because there's more than one way to solve it). To me you are apparently solving a problem similar to the arms race problem.
my guess is that you are reading about using a specific method of solving a system of ODE which employs a eigenvalue solution modified for ODE (note it's not the only way to solve it, and perhaps not popular). the steps are not straight forward (require analysis of each outcome during the process?) and there isn't a way to "force mm" to use that method (mm will use whichever method it finds determines will best completely solve it). it would maybe be best not to use mm for the lesson (do by hand) since it may take much longer to lay it all in than it is worth and you'll need to move on to the next/other methods quickly.
