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Most second-order Ordinary Differential Equations (ODES) arising in realistic applications such as applied mathematics, physics, metrology and engineering. All of these disciplines are concerned with the properties of differential equations of various types. ODES cannot be solved exactly. For these problems one does a qualitative analysis to get a rough idea of the behavior of the solution. Then a numerical method is employed to get an accurate solution. In this way, one can verify the answer obtained from the numerical method by comparing it to the answer obtained from qualitative analysis. In a few fortunate cases a second-order ode can be solved exactly. Because of the big efforts needed to solve second order linear ODES, some MATLAB methods were investigated, the result of these methods were studied and some judgment were done regarding the results accuracy and implementation time.

Evaluation of MATLAB Methods used to Solve Second Order Linear ODE