This paper mainly studies the solution and application of second order ordinary differential equations, and the different solving methods of these equations with constant coefficient and variable coefficient are separately discussed, which include the characteristic roots method of the second order ordinary differential equation and the specific solving method for different specific forms of the equations. There are methods of depression of order and variation of constants for the variable ordinary differential equation etc., and the second order ordinary differential equation is extensively applied in the fields of physics, mechanics and engineering technology.
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