What is the solution for (D^3+D^2-2D+12)y=0 ?

The solution for (D^3+D^2-2D+12)y=0 is y=c_{1}e^{-3x}+e^x(c_{2}cos(sqrt(3)x)+c_{3}sin(sqrt(3)x))

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(D^3+D^2-2D+12)y=0

(D^{3} + D^{2} - 2 D + 12) y = 0

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

Solution steps

(D^{3} + D^{2} - 2 D + 12) y = 0

Solve linear ODE:

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

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

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

y^{^{''}} + y = 0, y (π) = 1, y (π) = - 5

9 y^{^{''}} - 4 y = 0, y^{1} (0) = e \frac{2 x}{3}

3 y^{^{''}} = 4 y^{^{'}}

y^{^{''}} + y^{^{'}} = - cy

What is the solution for (D^3+D^2-2D+12)y=0 ?
The solution for (D^3+D^2-2D+12)y=0 is y=c_{1}e^{-3x}+e^x(c_{2}cos(sqrt(3)x)+c_{3}sin(sqrt(3)x))