What is the solution for (d^2y)/(dt^2)+8(dy)/(dt)+4y=0 ?

The solution for (d^2y)/(dt^2)+8(dy)/(dt)+4y=0 is y=c_{1}e^{2(sqrt(3)-2)t}+c_{2}e^{-2(2+sqrt(3))t}

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(d^2y)/(dt^2)+8(dy)/(dt)+4y=0

\frac{d ^{2} y}{d t ^{2}} + 8 \frac{d y}{d t} + 4 y = 0

y = c_{1} e^{2 (3 - 2) t} + c_{2} e^{- 2 (2 + 3) t}

Solution steps

\frac{d ^{2} y}{d t ^{2}} + 8 \frac{d y}{d t} + 4 y = 0

Solve linear ODE:

y = c_{1} e^{2 (3 - 2) t} + c_{2} e^{- 2 (2 + 3) t}

y = c_{1} e^{2 (3 - 2) t} + c_{2} e^{- 2 (2 + 3) t}

20 x^{^{''}} + 9 x^{^{'}} + x = 0, x (0) = 0, x^{^{'}} (0) = 4

y^{^{'''}} + y^{^{''}} - 7 y^{^{'}} + 5 y = 0

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

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

(y^{^{''}} - a y^{^{'}}) = b y

What is the solution for (d^2y)/(dt^2)+8(dy)/(dt)+4y=0 ?
The solution for (d^2y)/(dt^2)+8(dy)/(dt)+4y=0 is y=c_{1}e^{2(sqrt(3)-2)t}+c_{2}e^{-2(2+sqrt(3))t}