What is the solution for 9y^{'''}+11y^{''}+4y^'-14y=0 ?

The solution for 9y^{'''}+11y^{''}+4y^'-14y=0 is y=c_{1}e^{(7t)/9}+e^{-t}(c_{2}cos(t)+c_{3}sin(t))

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9y^{'''}+11y^{''}+4y^'-14y=0

9 y^{^{'''}} + 11 y^{^{''}} + 4 y^{^{'}} - 14 y = 0

y = c_{1} e^{\frac{7 t}{9}} + e^{- t} (c_{2} cos (t) + c_{3} sin (t))

Solution steps

9 y^{'''} (t) + 11 y^{''} (t) + 4 y^{'} (t) - 14 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{7 t}{9}} + e^{- t} (c_{2} cos (t) + c_{3} sin (t))

y = c_{1} e^{\frac{7 t}{9}} + e^{- t} (c_{2} cos (t) + c_{3} sin (t))

What is the solution for 9y^{'''}+11y^{''}+4y^'-14y=0 ?
The solution for 9y^{'''}+11y^{''}+4y^'-14y=0 is y=c_{1}e^{(7t)/9}+e^{-t}(c_{2}cos(t)+c_{3}sin(t))