DStabilityConditions
DStabilityConditions[eqn, x[t], t] gives the fixed points and stability conditions for a differential equation.
DStabilityConditions[{eqn1, eqn2, ...}, {x1[t], x2[t], ...}, t] gives the fixed points and stability conditions for a system of differential equations.
DStabilityConditions[{eqn1, eqn2, ...}, {x1[t], x2[t], ...}, t, {pnt1, pnt2, ...}] gives the stability conditions for the given fixed points.
Examples
Find stability conditions:
DStabilityConditions[x'[t] == x[t] (1 - x[t]), x[t], t]Please visit the official Wolfram Language Reference for more details.