What is the solution for 6y^{''''}+77y^{''}+255y=0 ?

The solution for 6y^{''''}+77y^{''}+255y=0 is

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6y^{''''}+77y^{''}+255y=0

6 y^{^{''''}} + 77 y^{^{''}} + 255 y = 0

y = e^{\frac{- 77 + 6 170 t}{2 ^{\frac{3}{2}} 3}} (c_{1} cos (\frac{191 t}{2 6 - 77 + 6 170}) + c_{2} sin (\frac{191 t}{2 6 - 77 + 6 170})) + e^{- \frac{- 77 + 6 170 t}{2 ^{\frac{3}{2}} 3}} (c_{3} cos (\frac{191 t}{2 6 - 77 + 6 170}) + c_{4} sin (\frac{191 t}{2 6 - 77 + 6 170}))

Solution steps

6 y^{(4)} (t) + 77 y^{''} (t) + 255 y = 0

Solve linear ODE:

y = e^{\frac{- 77 + 6 170 t}{2 ^{\frac{3}{2}} 3}} (c_{1} cos (\frac{191 t}{2 6 - 77 + 6 170}) + c_{2} sin (\frac{191 t}{2 6 - 77 + 6 170})) + e^{- \frac{- 77 + 6 170 t}{2 ^{\frac{3}{2}} 3}} (c_{3} cos (\frac{191 t}{2 6 - 77 + 6 170}) + c_{4} sin (\frac{191 t}{2 6 - 77 + 6 170}))

y = e^{\frac{- 77 + 6 170 t}{2 ^{\frac{3}{2}} 3}} (c_{1} cos (\frac{191 t}{2 6 - 77 + 6 170}) + c_{2} sin (\frac{191 t}{2 6 - 77 + 6 170})) + e^{- \frac{- 77 + 6 170 t}{2 ^{\frac{3}{2}} 3}} (c_{3} cos (\frac{191 t}{2 6 - 77 + 6 170}) + c_{4} sin (\frac{191 t}{2 6 - 77 + 6 170}))

What is the solution for 6y^{''''}+77y^{''}+255y=0 ?
The solution for 6y^{''''}+77y^{''}+255y=0 is