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Consider a linear non-homogeneous ordinary differential equation with constant coefficients  where  the ODE can be rewritten as  Thus, the particular solution is  The particular solution can be easily obtained, if the effects of the inverse operator Inverse Operation of Common Functions:
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Pros and Cons of the Method of Inverse Operators: The method of inverse operators can systematically solve some tough problems. However, if |
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Ordinary Differential Equations |
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ODE Home |
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General Terms |
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First Order ODE |
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Higher Order ODE |
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Homogen. Const. Coeff. |
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Non-homogen. C. C. |
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Variable Coeff. ODE |
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Particular Solution by |
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Undetermined Coeff. |
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Variation of Parameters |
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Reduction of Order |
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Inverse Operators |
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Systems of ODE |
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Sturm-Liouville |
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Transform Methods |
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Numerical Methods |
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Resources |
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Bibliography |
are all constants and 
. Let
have been studied in advance.
contains products of several simple functions e.g., 
, the method of inverse operators may be more tedious than the method of undetermined coefficients.
