What is the solution for (D^3+D^2+D+1)y=0 ?

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

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(D^3+D^2+D+1)y=0

(D^{3} + D^{2} + D + 1) y = 0

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

Solution steps

(D^{3} + D^{2} + D + 1) y = 0

Solve linear ODE:

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

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

y^{^{''}} - 2 y^{^{'}} - 8 y = 0, y (1) = 1, y^{^{'}} (1) = 0

y^{^{''}} + 16 y = 0, y (π) = 0, y (0) = 0

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

y^{^{''}} + 8 y^{^{'}} + 16 y = 0, y (0) = 6, y^{^{'}} (0) = 2

y^{^{''}} + 121 y = 0, y (0) = sin (k t)

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