Direct formulae for finding particular integral of certain ordinary differential equations with constant coefficients

This paper deals with simple and direct formulae for finding particular integrals of certain differential equations with constant coefficients. These results are contained in an unpublished work ‘Differentiation by a method of Continued Differentiation’ by author's Father (Late) Parameswara Iyer N Vaikom. Solution of equations of the form f(D)y = f(x).ϕ(x); where f(x) is n^th degree polynomial and ϕ(x) is sin ax,cos ax, e^x,sinh ax or cosh ax are dealt with.