What is the solution for y^{''}+6y^'+8.96y=0 ?

The solution for y^{''}+6y^'+8.96y=0 is y=c_{1}e^{-(14t)/5}+c_{2}e^{-(16t)/5}

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y^{''}+6y^'+8.96y=0

y^{^{''}} + 6 y^{^{'}} + 8.96 y = 0

y = c_{1} e^{- \frac{14 t}{5}} + c_{2} e^{- \frac{16 t}{5}}

Solution steps

y^{''} (t) + 6 y^{'} (t) + 8.96 y = 0

Solve linear ODE:

y = c_{1} e^{- \frac{14 t}{5}} + c_{2} e^{- \frac{16 t}{5}}

y = c_{1} e^{- \frac{14 t}{5}} + c_{2} e^{- \frac{16 t}{5}}

y^{^{''}} + 2 y^{^{'}} + 1.25 y = 0

y^{^{''}} + 20 y^{^{'}} + 36 y = 0, y (0) = 3, y^{^{'}} (0) = 0

3 \frac{d ^{2} y}{d x ^{2}} + 6 \frac{d y}{d x} + 3 y = 0

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

y^{^{'''}} - 7 y^{^{''}} + y^{^{'}} + 12 y = 0

What is the solution for y^{''}+6y^'+8.96y=0 ?
The solution for y^{''}+6y^'+8.96y=0 is y=c_{1}e^{-(14t)/5}+c_{2}e^{-(16t)/5}