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Differential equation is defined in the domain except at few points (may be consider the time domain ti ) may be (finite or countable) in the domain and a function or difference equation is defined at each ti in the domain. So, differential equation with the impulsive effects we call it as impulsive differential equation (IDE). The solutions of the differential equation is continuous in the domain. But the solutions of the IDE are piecewise continuous in the domain. This is due to the nature of impulsive system. Generally IDE have first order discontinuity. There are so many applications for IDE in practical life.

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Q: What is impulsive differential equation?
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