What is the solution for (d^3+8)y=0 ?

The solution for (d^3+8)y=0 is y=c_{1}e^{-2x}+e^x(c_{2}cos(sqrt(3)x)+c_{3}sin(sqrt(3)x))

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(d^3+8)y=0

(d^{3} + 8) y = 0

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

Solution steps

(d^{3} + 8) y = 0

Solve linear ODE:

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

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

y^{^{''}} + 3 y = 0, y (0) = 4, y^{^{'}} (0) = - 3

y^{^{''}} - 11 y^{^{'}} + 24 y = 0, y^{^{'}} (0) = 12

\frac{d ^{8} y}{d x ^{8}} - 8 \frac{d ^{4} y}{d x ^{4}} + 16 y = 0

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

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

What is the solution for (d^3+8)y=0 ?
The solution for (d^3+8)y=0 is y=c_{1}e^{-2x}+e^x(c_{2}cos(sqrt(3)x)+c_{3}sin(sqrt(3)x))