What is the solution for 100y^{'''}+60y^{''}+9y^'=0 ?

The solution for 100y^{'''}+60y^{''}+9y^'=0 is y=c_{1}+c_{2}e^{-(3t)/(10)}+c_{3}e^{-(3t)/(10)}t

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100y^{'''}+60y^{''}+9y^'=0

100 y^{^{'''}} + 60 y^{^{''}} + 9 y^{^{'}} = 0

y = c_{1} + c_{2} e^{- \frac{3 t}{10}} + c_{3} e^{- \frac{3 t}{10}} t

Solution steps

100 y^{'''} (t) + 60 y^{''} (t) + 9 y^{'} (t) = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{- \frac{3 t}{10}} + c_{3} e^{- \frac{3 t}{10}} t

y = c_{1} + c_{2} e^{- \frac{3 t}{10}} + c_{3} e^{- \frac{3 t}{10}} t

8 y - 2 y^{^{'}} + 6 y^{^{''}} - y^{^{'}} = 0

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y^{^{'}} 0 = (3), y (0) = 0

y^{^{''}} - (a + 1) y^{^{'}} + a y = 0

y^{^{''''}} - 2 y = 0

y^{^{''}} - 4 y^{^{'}} + 12 y = 0

What is the solution for 100y^{'''}+60y^{''}+9y^'=0 ?
The solution for 100y^{'''}+60y^{''}+9y^'=0 is y=c_{1}+c_{2}e^{-(3t)/(10)}+c_{3}e^{-(3t)/(10)}t