What is the solution for y^{''}+5y^'+8y=0 ?

The solution for y^{''}+5y^'+8y=0 is y=e^{-(5t)/2}(c_{1}cos((sqrt(7)t)/2)+c_{2}sin((sqrt(7)t)/2))

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y^{''}+5y^'+8y=0

y^{^{''}} + 5 y^{^{'}} + 8 y = 0

y = e^{- \frac{5 t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2}))

Solution steps

y^{''} (t) + 5 y^{'} (t) + 8 y = 0

Solve linear ODE:

y = e^{- \frac{5 t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2}))

y = e^{- \frac{5 t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2}))

y^{^{'''}} - 19 y^{^{'}} + 30 y = 0

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

y^{^{''}} + 5 y^{^{'}} - 6 y = 0, y (0) = - 3, y^{^{'}} (0) = 39

y^{^{'''''}} - 8 y^{^{'''}} + 16 y^{^{'}} = 0

y^{^{''}} + (\frac{0.5}{2}) y = 0

What is the solution for y^{''}+5y^'+8y=0 ?
The solution for y^{''}+5y^'+8y=0 is y=e^{-(5t)/2}(c_{1}cos((sqrt(7)t)/2)+c_{2}sin((sqrt(7)t)/2))