What is the solution for y^{''}+7y^'+16y=0 ?

The solution for y^{''}+7y^'+16y=0 is y=e^{-(7t)/2}(c_{1}cos((sqrt(15)t)/2)+c_{2}sin((sqrt(15)t)/2))

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y^{''}+7y^'+16y=0

y^{^{''}} + 7 y^{^{'}} + 16 y = 0

y = e^{- \frac{7 t}{2}} (c_{1} cos (\frac{15 t}{2}) + c_{2} sin (\frac{15 t}{2}))

Solution steps

y^{''} (t) + 7 y^{'} (t) + 16 y = 0

Solve linear ODE:

y = e^{- \frac{7 t}{2}} (c_{1} cos (\frac{15 t}{2}) + c_{2} sin (\frac{15 t}{2}))

y = e^{- \frac{7 t}{2}} (c_{1} cos (\frac{15 t}{2}) + c_{2} sin (\frac{15 t}{2}))

y^{^{''}} + α 2 y^{^{'}} + 2 y = 0

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

\frac{d ^{2} y}{d x ^{2}} = - 36 y

y^{^{''}} - 6 y^{^{'}} + 25 y = 0, y (0) = - 3, y^{^{'}} (0) = - 1

y^{^{''}} + \frac{100}{1} y^{^{'}} = 0

What is the solution for y^{''}+7y^'+16y=0 ?
The solution for y^{''}+7y^'+16y=0 is y=e^{-(7t)/2}(c_{1}cos((sqrt(15)t)/2)+c_{2}sin((sqrt(15)t)/2))