On Solutions of Second Order Differential Equations

Abstract

Our aim in this work is to give the general form for finding the generalsolution to the differential equation which has the form y″+ p (x) y'+ Q(x) y =0 and its proofs by using the assumption   Z x dx y e ( ) whichchanges the above equation to Riccati equation which has the formZ' +Z² + p (x) Z+ Q(x) = 0 .IntroductionMany researchers in the field of differential equations and others, may facethe problem of solving some differential equations whose solutions aredifficult to find by using the simple methods . Therefore , they are trying tosolve these equations by the power series or the Frobenius method [7] .Mohammed [4] faced difficulties in solving equations with the followingforms