What is the solution for (D^2-3D+2)(D^2+2D+1)y=x ?

The solution for (D^2-3D+2)(D^2+2D+1)y=x is y=c_{1}e^x+c_{2}e^{2x}+c_{3}e^{-x}+c_{4}xe^{-x}+x/2-1/4

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(D^2-3D+2)(D^2+2D+1)y=x

(D^{2} - 3 D + 2) (D^{2} + 2 D + 1) y = x

y = c_{1} e^{x} + c_{2} e^{2 x} + c_{3} e^{- x} + c_{4} x e^{- x} + \frac{x}{2} - \frac{1}{4}

Solution steps

(D^{2} - 3 D + 2) (D^{2} + 2 D + 1) y = x

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{2 x} + c_{3} e^{- x} + c_{4} x e^{- x} + \frac{x}{2} - \frac{1}{4}

y = c_{1} e^{x} + c_{2} e^{2 x} + c_{3} e^{- x} + c_{4} x e^{- x} + \frac{x}{2} - \frac{1}{4}

What is the solution for (D^2-3D+2)(D^2+2D+1)y=x ?
The solution for (D^2-3D+2)(D^2+2D+1)y=x is y=c_{1}e^x+c_{2}e^{2x}+c_{3}e^{-x}+c_{4}xe^{-x}+x/2-1/4