What is the solution for 6y^{'''}+78y^'-696y=0 ?

The solution for 6y^{'''}+78y^'-696y=0 is y=c_{1}e^{4t}+e^{-2t}(c_{2}cos(5t)+c_{3}sin(5t))

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6y^{'''}+78y^'-696y=0

6 y^{^{'''}} + 78 y^{^{'}} - 696 y = 0

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

Solution steps

6 y^{'''} (t) + 78 y^{'} (t) - 696 y = 0

Solve linear ODE:

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

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

y^{^{''}} - \frac{1}{a ^{2}} y = 0

y^{^{''}} + y^{^{'}} - 6 y = 0, y (0) = - 3

x^{^{''}} + 6 x^{^{'}} + 3 x = 0, x^{^{'}} (0) = 1, x (0) = 2

y^{^{'''}} + 3 y + 4 y = 0

y^{^{''}} - a y^{^{'}} + y = 0

What is the solution for 6y^{'''}+78y^'-696y=0 ?
The solution for 6y^{'''}+78y^'-696y=0 is y=c_{1}e^{4t}+e^{-2t}(c_{2}cos(5t)+c_{3}sin(5t))