Advanced Applied Mathematics - Super Position Theorem (formed linear combination) and use of Undetermined Coefficients solved a third-order non-homogeneous differential equation

I found the solution to a third-order non-homogeneous differential equation (made use of the Super Position Theorem) by using the method of Undetermined Coefficients, where this solution is (obviously) the complimentary solution and particular solution sum.

This solution can be checked and verified (with the use of MATLAB) provided verification that this solution is the correct solution to the given problem shown in the photos featured above.

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