What is the solution for (d^2y)/(dt^2)+2(dy)/(dt)+10y=0 ?

The solution for (d^2y)/(dt^2)+2(dy)/(dt)+10y=0 is y=e^{-t}(c_{1}cos(3t)+c_{2}sin(3t))

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(d^2y)/(dt^2)+2(dy)/(dt)+10y=0

\frac{d ^{2} y}{d t ^{2}} + 2 \frac{d y}{d t} + 10 y = 0

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

Solution steps

\frac{d ^{2} y}{d t ^{2}} + 2 \frac{d y}{d t} + 10 y = 0

Solve linear ODE:

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

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

y^{^{''}} - 3 y^{^{'}} = 0

3 \frac{d ^{2} y}{d x ^{2}} + 7 \frac{d y}{d x} - 11 y = 0

y^{^{''}} - 7 y^{^{'}} + 12 y = 0, y (0) = 0, y^{^{'}} (1) = e^{3}

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

(2 D^{4} - 3 D^{3} - 2 D^{2}) y = 0

What is the solution for (d^2y)/(dt^2)+2(dy)/(dt)+10y=0 ?
The solution for (d^2y)/(dt^2)+2(dy)/(dt)+10y=0 is y=e^{-t}(c_{1}cos(3t)+c_{2}sin(3t))