What is the solution for (D^2-3D+2)y=72xe^{-x} ?

The solution for (D^2-3D+2)y=72xe^{-x} is y=c_{1}e^{2x}+c_{2}e^x+12xe^{-x}+10e^{-x}

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(D^2-3D+2)y=72xe^{-x}

(D^{2} - 3 D + 2) y = 72 x e^{- x}

y = c_{1} e^{2 x} + c_{2} e^{x} + 12 x e^{- x} + 10 e^{- x}

Solution steps

(D^{2} - 3 D + 2) y = 72 x e^{- x}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} + 12 x e^{- x} + 10 e^{- x}

y = c_{1} e^{2 x} + c_{2} e^{x} + 12 x e^{- x} + 10 e^{- x}

y^{^{''}} + 6 y^{^{'}} + 8 = (3 x - 2) e^{4 x}

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{- 4 t}, y (0) = 1, y (0) = 5

y^{^{''}} + 3 y^{^{'}} = x^{2}

\frac{d ^{2} y}{d x ^{2}} + 9 y = sin (3 x)

y^{^{''}} + 4 y^{^{'}} + 3 y = cos (t)

What is the solution for (D^2-3D+2)y=72xe^{-x} ?
The solution for (D^2-3D+2)y=72xe^{-x} is y=c_{1}e^{2x}+c_{2}e^x+12xe^{-x}+10e^{-x}