Please solve this problem for me. Please break it down step by step. DO NOT answer if your answer is not exact as the one below.
Problem: y^(5th derivative) + 18y^(3rd derivative) + 81y' = x^2 * sin(3x)
The correct answer is [Ax^5 + Bx^3 + Cx^2]cos(3x) + [Dx^5 + Ex^3 + Fx^2]sin(3x).
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