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Constant Coefficients and Maple Verification

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Could you work out the problem and also add the Maple verification if possible? Please see the full problem description in attached PDF.

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The expert examines constant coefficients and maple verification.

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1.
The equation is:
(1.1)
The associated homogenous equation is:
(1.2)
We "guess" a homogenous solution in the form:
(1.3)
When we plug it into (1.2) we get the incidental equation.

(1.4)
Note that the coefficient of the nth power of r corresponds with the coefficient of the nth order derivative.
 
The solutions to equation (1.4) are:

(1.5)
Thus, the two homogenous solutions are:
(1.6)
Now we need to find a particular solution to the non-homogenous equation.
We note that the non homogenous term is in itself a solution of a homogenous equation with constant coefficients ( ) so we can use the method of undetermined coefficients.
We set the ...

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