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

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\frac{d}{d x} (e^{3 x} + e^{- 2 x})

y^{^{''}} + 6 y^{^{'}} + 15 y = 0

\int (3 t^{4} - 8) t^{3} d t

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