### On Solutions of Second Order Differential Equations

*Al-Qadisiyah Journal of Pure Science*

2007, Volume 12, Issue 1, Pages 322-337

2007, Volume 12, Issue 1, Pages 322-337

#### 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

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