What is the solution for (D^4-D^3-3D+D+2)y=0 ?

The solution for (D^4-D^3-3D+D+2)y=0 is

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(D^4-D^3-3D+D+2)y=0

(D^{4} - D^{3} - 3 D + D + 2) y = 0

y = c_{1} e^{x} + c_{2} e^{32 x} + e^{- \frac{x}{2 ^{\frac{2}{3}}}} (c_{3} cos (\frac{3 2 ^{\frac{2}{3}} x}{2}) + c_{4} sin (\frac{3 2 ^{\frac{2}{3}} x}{2}))

Solution steps

(D^{4} - D^{3} - 3 D + D + 2) y = 0

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{32 x} + e^{- \frac{x}{2 ^{\frac{2}{3}}}} (c_{3} cos (\frac{3 2 ^{\frac{2}{3}} x}{2}) + c_{4} sin (\frac{3 2 ^{\frac{2}{3}} x}{2}))

y = c_{1} e^{x} + c_{2} e^{32 x} + e^{- \frac{x}{2 ^{\frac{2}{3}}}} (c_{3} cos (\frac{3 2 ^{\frac{2}{3}} x}{2}) + c_{4} sin (\frac{3 2 ^{\frac{2}{3}} x}{2}))

81 y^{^{''}} = - 16 y, y (0) = cos (k t)

3 y^{^{''}} - 15 y^{^{'}} + 18 y = 0

y^{^{'''}} + 5 y^{^{''}} - 4 y^{^{'}} - 60 y = 0

25 y^{^{''}} + 10 y^{^{'}} + y = 0, y (0) = 2, y^{^{'}} (0) = 1

y^{^{''}} + 10 y^{^{'}} + 26 y = 0, y (0) = 1, y^{^{'}} (0) = 0

What is the solution for (D^4-D^3-3D+D+2)y=0 ?
The solution for (D^4-D^3-3D+D+2)y=0 is