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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

x^{^{''}} + c^{2} x = 0

y^{^{''}} + 4 y^{^{'}} + 40 y = 0, y (0) = 0, y^{^{'}} (0) = 0

x^{^{''}} - 0.5 x = 0

y^{^{''}} + 36 y = 0, y (0) = - 5, y^{^{'}} (0) = 12

y^{^{'''''}} - 16 y^{^{'}} = 0

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