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

The solution for (D^2+2D^2+D+2)y=0 is y=e^{-x/6}(c_{1}cos((sqrt(23)x)/6)+c_{2}sin((sqrt(23)x)/6))

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

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

y = e^{- \frac{x}{6}} (c_{1} cos (\frac{23 x}{6}) + c_{2} sin (\frac{23 x}{6}))

Solution steps

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

Solve linear ODE:

y = e^{- \frac{x}{6}} (c_{1} cos (\frac{23 x}{6}) + c_{2} sin (\frac{23 x}{6}))

y = e^{- \frac{x}{6}} (c_{1} cos (\frac{23 x}{6}) + c_{2} sin (\frac{23 x}{6}))

What is the solution for (D^2+2D^2+D+2)y=0 ?
The solution for (D^2+2D^2+D+2)y=0 is y=e^{-x/6}(c_{1}cos((sqrt(23)x)/6)+c_{2}sin((sqrt(23)x)/6))