What is the solution for 16y^{'''}+24y^{''}+9y^'=0 ?

The solution for 16y^{'''}+24y^{''}+9y^'=0 is y=c_{1}+c_{2}e^{-(3t)/4}+c_{3}e^{-(3t)/4}t

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16y^{'''}+24y^{''}+9y^'=0

16 y^{^{'''}} + 24 y^{^{''}} + 9 y^{^{'}} = 0

y = c_{1} + c_{2} e^{- \frac{3 t}{4}} + c_{3} e^{- \frac{3 t}{4}} t

Solution steps

16 y^{'''} (t) + 24 y^{''} (t) + 9 y^{'} (t) = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{- \frac{3 t}{4}} + c_{3} e^{- \frac{3 t}{4}} t

y = c_{1} + c_{2} e^{- \frac{3 t}{4}} + c_{3} e^{- \frac{3 t}{4}} t

121 y^{^{''}} - 4 y = 0

64 y^{^{''}} + 176 y^{^{'}} + 121 y = 0

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

y^{^{'''}} - 10 y^{^{''}} + 25 y^{^{'}} = 0

y^{^{''}} - 211 y^{^{'}} + 11 y = 0

What is the solution for 16y^{'''}+24y^{''}+9y^'=0 ?
The solution for 16y^{'''}+24y^{''}+9y^'=0 is y=c_{1}+c_{2}e^{-(3t)/4}+c_{3}e^{-(3t)/4}t