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2. [20 scores max] Consider the Cauchy problem for the second-order linear equation y - 9y = 2xe3x, y(0) = -3, y' (0)=-1/18 a. Find

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2. [20 scores max] Consider the Cauchy problem for the second-order linear equation y" - 9y = 2xe3x, y(0) = -3, y' (0)=-1/18 a. Find the general solution of the corresponding homogeneous equation. b. Find the particular solution of the non-homogeneous equation using the method of undetermined coefficients. c. Find the solution of the Cauchy

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