  This work investigates a new approach to find closed form analytical
approximate solution of linear initial value problems. Classical Bernoulli
polynomials have been used to derive a finite set of orthonormal polynomials
and a finite operational matrix to simplify derivatives of dependent variable.
These orthonormal polynomials together with the operational matrix of relevant
order provides a good approximation to the solution of a linear initial value
problem. Depending upon the nature of a problem, a series form approximation or
numerical approximation can be obtained. The technique has been demonstrated
through three problems. Approximate solutions have been compared with available
exact or other numerical solutions. High degree of accuracy has been noted in
numerical values of solutions for considered problems.
