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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{d}{d x} (\frac{x}{( x - 9 ) ^{2}})

\frac{d}{d x} (\frac{8 x ^{2} + 9}{x ^{2} + 1})

\frac{\partial}{\partial y} (\frac{1}{2} y)

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6 y^{^{''}} + 11 y^{^{'}} - 2 y = 0

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