What is the solution for y+2y^{'''}+10y^{''}+18y^'+9y=0 ?

The solution for y+2y^{'''}+10y^{''}+18y^'+9y=0 is y=c_{1}e^{-t}+e^{-2t}(c_{2}cos(t)+c_{3}sin(t))

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y+2y^{'''}+10y^{''}+18y^'+9y=0

y + 2 y^{^{'''}} + 10 y^{^{''}} + 18 y^{^{'}} + 9 y = 0

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

Solution steps

y + 2 y^{'''} (t) + 10 y^{''} (t) + 18 y^{'} (t) + 9 y = 0

Solve linear ODE:

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

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

y^{^{''}} + 16 y = 0, y (0) = 1, y^{^{'}} (1) = 0

y^{^{''}} + 16 y = 0, y (0) = 1, y (1) = 0

2 y^{^{''}} + 9 y^{^{'}} + 7 y = 0

9 y^{^{''}} - 64 y = 0, y (0) = 1, y^{^{'}} (0) = 0

5 y^{^{''}} + 21 y^{^{'}} + 4 y = 0, y (0) = 1, y^{^{'}} (0) = - 19.2 y

What is the solution for y+2y^{'''}+10y^{''}+18y^'+9y=0 ?
The solution for y+2y^{'''}+10y^{''}+18y^'+9y=0 is y=c_{1}e^{-t}+e^{-2t}(c_{2}cos(t)+c_{3}sin(t))