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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{1}{16} x^{^{''}} + 2 x^{^{'}} + x = 0

y^{^{''}} - 4 y^{^{'}} + 3 y = 0, y (0) = 6, y^{^{'}} (0) = 10

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

y^{^{''}} + 6 y^{^{'}} + 25 y = 0, y (0) = 3, y^{^{'}} (0) = 7

D^{2} (D + 3)^{2} y = 0

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