2. The 8th-order homogeneous linear, constant coefficients differential equation y(8) – y(7) – 5y(0) +11y(5) – 22y" + 24y/" – 8y/ = 0 has characteristic equation as follows. (x² – 2A + 2) (A – 1)° (A + 2)² A = 0 (a) Write the general solution to the above homogeneous differential equation (b) Write the form of the non-homogeneous solution Y„(x) used in the method of undeter- mined coefficients to solve the non-homogeneous differential equation defined below y(8) – y(7) – 5y(®) +11y(®) – 22y" + 24y" – 8y' = f(x) where f (x) = e" (x sin a + cos 2x + x) + xe' -2x +1 (Do not plug into the differential equation to solve for the coefficients. Just put the form only)
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