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For a delay differential equationx  ¨    (  t  )  +  a  (  t  )    x  ˙    (  t  )  +    ∑   k  =  1   m    b  k   (  t  )  x  (   g  k   (  t  )  )  =  0  ,   g  k   (  t  )  ≤  t  ,$$\ddot{x}(t) + a(t)\dot{x}(t)+ \displaystyle\sum\limits_{k=1}^m b_k(t)x(g_k(t))=0, g_k(t)\leq t, $$a generalized Riccati inequality is constructed for nonoscillation and exponential stability of the differential equation.

Nonoscillation and exponential stability of the second order delay differential equation with damping