What is the solution for (d^3+9d^2+27d+27)y=0 ?

The solution for (d^3+9d^2+27d+27)y=0 is y=c_{1}e^{-3x}+c_{2}xe^{-3x}+c_{3}x^2e^{-3x}

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(d^3+9d^2+27d+27)y=0

(d^{3} + 9 d^{2} + 27 d + 27) y = 0

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

Solution steps

(d^{3} + 9 d^{2} + 27 d + 27) y = 0

Solve linear ODE:

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

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

(D^{2} - D - 2) y = 0

y^{^{''}} + 5 y^{^{'}} - 36 y = 0, y (0) = α, y^{^{'}} (0) = - 72

y^{^{''}} - 3 y^{^{'}} - 4 y = 0, y (0) = 1, y^{^{'}} (0) = 29

y^{^{''}} + (\frac{9.8}{0.06}) y = 0

16 y - 8 y^{^{'}} = y^{^{''}}

What is the solution for (d^3+9d^2+27d+27)y=0 ?
The solution for (d^3+9d^2+27d+27)y=0 is y=c_{1}e^{-3x}+c_{2}xe^{-3x}+c_{3}x^2e^{-3x}