What is the solution for x^{'''}+9*x^{''}+x^'+9x=0 ?

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

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x^{'''}+9*x^{''}+x^'+9x=0

x^{^{'''}} + 9 \cdot x^{^{''}} + x^{^{'}} + 9 x = 0

x = c_{1} e^{- 9 t} + c_{2} cos (t) + c_{3} sin (t)

Solution steps

x^{'''} (t) + 9 \cdot x^{''} (t) + x^{'} (t) + 9 x = 0

Solve linear ODE:

x = c_{1} e^{- 9 t} + c_{2} cos (t) + c_{3} sin (t)

x = c_{1} e^{- 9 t} + c_{2} cos (t) + c_{3} sin (t)

(D^{2} + 9) y = 0

(D^{3} - 3 D^{2} - 10 D) y = 0

y^{^{''}} + 25 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - 36 y = 0, y (\frac{π}{4}) = 1, y^{^{'}} (\frac{π}{4}) = - 2

y^{^{''}} + 3 y^{^{'}} - y = 0, y (1) = 2, y^{^{'}} (1) = 0

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