What is the solution for y^{'''}+6y^{''}-11y^'-116y=0 ?

The solution for y^{'''}+6y^{''}-11y^'-116y=0 is y=c_{1}e^{4t}+e^{-5t}(c_{2}cos(2t)+c_{3}sin(2t))

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y^{'''}+6y^{''}-11y^'-116y=0

y^{^{'''}} + 6 y^{^{''}} - 11 y^{^{'}} - 116 y = 0

y = c_{1} e^{4 t} + e^{- 5 t} (c_{2} cos (2 t) + c_{3} sin (2 t))

Solution steps

y^{'''} (t) + 6 y^{''} (t) - 11 y^{'} (t) - 116 y = 0

Solve linear ODE:

y = c_{1} e^{4 t} + e^{- 5 t} (c_{2} cos (2 t) + c_{3} sin (2 t))

y = c_{1} e^{4 t} + e^{- 5 t} (c_{2} cos (2 t) + c_{3} sin (2 t))

What is the solution for y^{'''}+6y^{''}-11y^'-116y=0 ?
The solution for y^{'''}+6y^{''}-11y^'-116y=0 is y=c_{1}e^{4t}+e^{-5t}(c_{2}cos(2t)+c_{3}sin(2t))