On Solutions of Second Order Differential Equations


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