Higher order differential equations are those with a derivative order greater than one.
See homogenous and wronskian for methods to classify the equation.
The homogeneous form of the differential equation can be used to find the general solution to find the particular solution and the total solution the method undetermined coefficients and variation-of-parameters can be used.
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Different methods have to be used depending on the equation. See homogenous and wronskian for methods to classify the equation.Depending on whether or not it is homogenous you will need to use different methods. See homogeneous-linear-differential-equations and #link