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Adkins Ordinary Differential Equations 1st. João Pedro. Download with Google Download with Facebook. or. Create a free account to download. Download Full PDF Package. For any value of c, an equilibrium of the linear second-order ordinary differential equation with constant coefficients x"(t) + ax'(t) + bx(t) = c with b ≠ 0 is stable if and only if the real parts of both roots of the characteristic equation r 2 + ar + b = 0 are negative, or, equivalently, if and only if a > 0 and b > 0.