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We establish the generalized superstability of differential equations of  nth-order with initial conditions and investigate the generalized  superstability of differential equations of second order in the form of  y′′(x) + p(x)y′(x)+q(x)y(x) = 0 and the superstability of linear differential  equations with constant coefficients with initial conditions.

On the generalized superstability of nth-order linear differential equations with initial conditions