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

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

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(D^3-1)y=0

(D^{3} - 1) y = 0

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

Solution steps

(D^{3} - 1) y = 0

Solve linear ODE:

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

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

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