Method of Undetermined Coefficients - Description of The Method

Description of The Method

Consider a linear non-homogeneous ordinary differential equation of the form

The method consists of finding the general homogeneous solution for the complementary linear homogeneous differential equation

and a particular integral of the linear non-homogeneous ordinary differential equation based on . Then the general solution to the linear non-homogeneous ordinary differential equation would be

If consists of the sum of two functions and we say that is the solution based on and the solution based on . Then, using a superposition principle, we can say that the particular integral is

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