What is the solution for 144y^{'''}+264y^{''}+121y^'=0 ?

The solution for 144y^{'''}+264y^{''}+121y^'=0 is y=c_{1}+c_{2}e^{-(11t)/(12)}+c_{3}e^{-(11t)/(12)}t

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144y^{'''}+264y^{''}+121y^'=0

144 y^{^{'''}} + 264 y^{^{''}} + 121 y^{^{'}} = 0

y = c_{1} + c_{2} e^{- \frac{11 t}{12}} + c_{3} e^{- \frac{11 t}{12}} t

Solution steps

144 y^{'''} (t) + 264 y^{''} (t) + 121 y^{'} (t) = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{- \frac{11 t}{12}} + c_{3} e^{- \frac{11 t}{12}} t

y = c_{1} + c_{2} e^{- \frac{11 t}{12}} + c_{3} e^{- \frac{11 t}{12}} t

y^{^{'''}} - y^{^{''}} = 8 y^{^{'''}}

4 y^{^{''}} - y = 0, y (- 2) = 1, y^{2} (- 2) = - 1

8 y^{^{''}} + 128 y = 0

y^{^{''}} + 2 y^{^{'}} + 35 y = 0, y (0) = - 3, y^{^{'}} (0) = 1

y^{^{'''}} - 4 y^{^{''}} - 11 y^{^{'}} + 30 y = 0

What is the solution for 144y^{'''}+264y^{''}+121y^'=0 ?
The solution for 144y^{'''}+264y^{''}+121y^'=0 is y=c_{1}+c_{2}e^{-(11t)/(12)}+c_{3}e^{-(11t)/(12)}t