Problems attached below, please include steps in your solution. Thanks. 10. Cons

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Problems attached below, please include steps in your solution. Thanks.

10. Consider the real, constant coefficient linear differential operator given below. L(D) = (D - 3)^3 (D2 + 4D + 13)^2 a) Find the general solution to the homogeneous differential equation Ly = 0. b) Write down the form for a particular solution to the non-homogeneous equation (D - 3)^3 (D2 + 4D + 13)^2 y = 4xe^-2x cos(3x) Do not try to solve for the coefficients! Your particular solution must not contain any terms that that are solutions of the homogeneous equation. Show that (D-1)^5 e^x (x^3+3x^4)=0

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