What is the solution for (d^2y)/(dt^2)+2(dy)/(dt)+7y=0 ?

The solution for (d^2y)/(dt^2)+2(dy)/(dt)+7y=0 is y=e^{-t}(c_{1}cos(sqrt(6)t)+c_{2}sin(sqrt(6)t))

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(d^2y)/(dt^2)+2(dy)/(dt)+7y=0

\frac{d ^{2} y}{d t ^{2}} + 2 \frac{d y}{d t} + 7 y = 0

y = e^{- t} (c_{1} cos (6 t) + c_{2} sin (6 t))

Solution steps

\frac{d ^{2} y}{d t ^{2}} + 2 \frac{d y}{d t} + 7 y = 0

Solve linear ODE:

y = e^{- t} (c_{1} cos (6 t) + c_{2} sin (6 t))

y = e^{- t} (c_{1} cos (6 t) + c_{2} sin (6 t))

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

y^{^{''}} + 3 y^{^{'}} + 4 y = 0, y (0) = 5, y^{^{'}} (0) = 2

2 y^{^{''}} - 4 y^{^{'}} + 13 y = 0

20 y^{^{''}} + 3 y^{^{'}} - 2 y = 0

3 \frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} - 8 y = 0

What is the solution for (d^2y)/(dt^2)+2(dy)/(dt)+7y=0 ?
The solution for (d^2y)/(dt^2)+2(dy)/(dt)+7y=0 is y=e^{-t}(c_{1}cos(sqrt(6)t)+c_{2}sin(sqrt(6)t))