Given the differential equation y" + 4y' - 12y 5x e7* And the Solutions to its Characteristic Equation Characteristic Solutions: R, = -6 and R, = 2 (1) Determine the General Form of the Particular Solution, and (2) Write the General Solution for the Particular Side of the Differential Equation. A y, = [Ax]e7* -6x B 'p = [Ax + B]e + [Cx + D]e2x y, = [Ax]e* cos(x) + [Bx]eT* sin(x) D) y, = [Ax + B]eT* E [Ax? + Bx] e7% Y, = [Ax3 + Bx?] e?x

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