What is the solution for 49y^{'''}+56y^{''}+16y^'=0 ?

The solution for 49y^{'''}+56y^{''}+16y^'=0 is y=c_{1}+c_{2}e^{-(4t)/7}+c_{3}e^{-(4t)/7}t

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49y^{'''}+56y^{''}+16y^'=0

49 y^{^{'''}} + 56 y^{^{''}} + 16 y^{^{'}} = 0

y = c_{1} + c_{2} e^{- \frac{4 t}{7}} + c_{3} e^{- \frac{4 t}{7}} t

Solution steps

49 y^{'''} (t) + 56 y^{''} (t) + 16 y^{'} (t) = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{- \frac{4 t}{7}} + c_{3} e^{- \frac{4 t}{7}} t

y = c_{1} + c_{2} e^{- \frac{4 t}{7}} + c_{3} e^{- \frac{4 t}{7}} t

\frac{d ^{3} y}{d x ^{3}} + 8 \frac{d y}{d x} = 0

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = 2, y^{^{'}} (0) = 5

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = 2, y^{^{'}} (0) = 4

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

x^{^{''}} + 96 x = 0

What is the solution for 49y^{'''}+56y^{''}+16y^'=0 ?
The solution for 49y^{'''}+56y^{''}+16y^'=0 is y=c_{1}+c_{2}e^{-(4t)/7}+c_{3}e^{-(4t)/7}t