Integral-based solution for a class of second order boundary value problems

An integral formulation for the solution of a class of second order boundary value problems which are described by the equation d²y/dx² + P(x,y, dy/dx, d²y/dx²) = 0, x ∈ (0,a), is presented. The resulting integral equations are then solved by expressing the dependent variable y as a power series which made the computation of various integrals possible. The proposed method is tested through some examples to show the applicability of the method to solve a wide range of second order differential equations including the nonlinear ones.