I have to check the stability of the equilibrium point of the system $$\frac{dx}{dt}=-x+\ln (|t|+1)y-\sin (t)z, \\ \frac{dy}{dt}=-\ln (|t|+1)x-y+e^tz, \\ \frac{dz}{dt}=\sin (t)x-e^ty-z$$
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The characteristic equation of the above system is $$\begin{vmatrix} -1-\kappa & \ln (|t|+1) & -\sin (t)\\ \ln (|t|+1) & -1-\kappa & e^t\\ \sin (t) & -e^t & -1-\kappa \end{vmatrix}=0$$
Do we have to find the eigenvalues and then would the stability depend on the sign of these eigenvalues?