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)

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)