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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''''}} - 4 y^{^{'''}} + 2 y^{^{''}} + 4 y^{^{'}} - 3 y = 0

y^{^{''''}} + y^{^{'''}} - 2 y^{^{''}} = 0

y^{^{'''}} - 6 y^{^{'}} + 11 y^{^{'}} - 6 y = 0

(D^{2} + 5 D + 6) y = 0

5000 x^{^{''}} + 105324.07 x = 0

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