The method of undetermined coefficients

Consider a differential equation [Maple Math] , where [Maple Math] and [Maple Math] are constants. If the function [Maple Math] is a product of one or more of the following: Polynomial, [Maple Math] , [Maple Math] or [Maple Math] then a particular solution has the similar form. We ilustrate this on several examples.

Example 1: Find a particular solution of [Maple Math] .

Example 2: Find a particular solution of [Maple Math] .

Example 3: Find a particular solution of [Maple Math] .

Sometimes no linear combination of [Maple Math] and [Maple Math] is a solution in which case we try the product [Maple Math] for some positive integer [Maple Math] . We ilustrate this on following exampe this on following examples.

Example 4: Find a particular solution of [Maple Math] .

Example 5: Find a particular solution of [Maple Math] .

Example 6: Find a particular solution of [Maple Math] .

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