What is the solution for d^2(d+3)^2y=9e^{-3x} ?

The solution for d^2(d+3)^2y=9e^{-3x} is y=c_{1}+c_{2}x+c_{3}e^{-3x}+c_{4}xe^{-3x}+(e^{-3x}x^2)/2

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d^2(d+3)^2y=9e^{-3x}

d^{2} (d + 3)^{2} y = 9 e^{- 3 x}

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

Solution steps

d^{2} (d + 3)^{2} y = 9 e^{- 3 x}

Solve linear ODE:

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

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

y^{^{''}} - 11 y = e^{x}

y^{^{''}} + 256 y = 16 cos (3 t)

y^{^{''}} - y^{^{'}} = 1 - 2 x

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

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

What is the solution for d^2(d+3)^2y=9e^{-3x} ?
The solution for d^2(d+3)^2y=9e^{-3x} is y=c_{1}+c_{2}x+c_{3}e^{-3x}+c_{4}xe^{-3x}+(e^{-3x}x^2)/2