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

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

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(d^2+d+1)y=0

(d^{2} + d + 1) y = 0

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

Solution steps

(d^{2} + d + 1) y = 0

Solve linear ODE:

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

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

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