試題詳解

5. (5%) Solve the equation y⁽⁵⁾ - y⁽⁴⁾ – 2y ⁽³⁾ + 2y" + y' = y. Which are the possible solutions?
(A)y = C₁e^x + c₂xe^x+C₃x²ex + C₄x³ex+c₅xe^-x
(B)y = C₁ex + C₂xe^x+C₃e^-x + C₄xe^-x+c₅x²e^-x
(C)y = C₁e^x + C₂xe^x+C₃e^-x + C4e^-2x+C₅xe-^2x
(D)y = c₁e^x + c₂xe^x+C3x²e^x + C₄e^-x+c₅xe^-x

(E) y = C₁e^x + C₂xe^x+C₃e^x + C₄e^2x+C₅e^-2x