What is the solution for 64y^{'''}+112y^{''}+49y^'=0 ?

The solution for 64y^{'''}+112y^{''}+49y^'=0 is y=c_{1}+c_{2}e^{-(7t)/8}+c_{3}e^{-(7t)/8}t

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64y^{'''}+112y^{''}+49y^'=0

64 y^{^{'''}} + 112 y^{^{''}} + 49 y^{^{'}} = 0

y = c_{1} + c_{2} e^{- \frac{7 t}{8}} + c_{3} e^{- \frac{7 t}{8}} t

Solution steps

64 y^{'''} (t) + 112 y^{''} (t) + 49 y^{'} (t) = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{- \frac{7 t}{8}} + c_{3} e^{- \frac{7 t}{8}} t

y = c_{1} + c_{2} e^{- \frac{7 t}{8}} + c_{3} e^{- \frac{7 t}{8}} t

y^{^{''}} = 5 y, y^{0} = - 2, y^{2} = 10

y^{^{''}} + 4 a^{2} y^{^{'}} + y = 0

y^{^{''}} - 2 y^{^{'}} + 5 y = 0, y (0) = - 1, y^{^{'}} (0) = 3

\frac{d ^{4} y}{d t ^{4}} - y = 0

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

What is the solution for 64y^{'''}+112y^{''}+49y^'=0 ?
The solution for 64y^{'''}+112y^{''}+49y^'=0 is y=c_{1}+c_{2}e^{-(7t)/8}+c_{3}e^{-(7t)/8}t