Abstract: In this paper,we study the solution of differential equation with Dirac function and Heaviside function, arising from discontinuous and impulsive excitation. Firstly, according to the theory of differential equation, we suggest x(t)=x₁(t) + x₂(t)H(t-a); then we derive the equation of x₁(t) and x₂ (t) by terms of property of distribution, and by solving x₁ (t) and x₂ (t) we obtain x(t); finally, we make a thorough investigation about periodic impulsive parametric excitation.

Key words: hybrid perturbation-Galerkin technique, circular cross-section tube with constriction, blood flow