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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{d ^{4} y}{d x ^{4}} - 14 \frac{d ^{2} y}{d x ^{2}} - 32 y = 0

y^{^{''}} + y^{^{'}} - 6 y = 0, y (0) = 1, y^{^{'}} (0) = 2

y^{^{'''}} + 3 y^{^{''}} + 2 y^{^{'}} = 0

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (0) = 1, y^{^{'}} (0) = 3

x^{^{''}} + 5 x^{^{'}} + 6 x = 0

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