What is the solution for (d^2y)/(dt^2)+6(dy)/(dt)+9y=0 ?

The solution for (d^2y)/(dt^2)+6(dy)/(dt)+9y=0 is y=c_{1}e^{-3t}+c_{2}te^{-3t}

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(d^2y)/(dt^2)+6(dy)/(dt)+9y=0

\frac{d ^{2} y}{d t ^{2}} + 6 \frac{d y}{d t} + 9 y = 0

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

Solution steps

\frac{d ^{2} y}{d t ^{2}} + 6 \frac{d y}{d t} + 9 y = 0

Solve linear ODE:

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

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

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

y^{^{''}} + n y = 0

y^{^{''}} + 4 y^{^{'}} + 20 y = 0, y (0) = 3, y^{^{'}} (0) = - 5

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

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

What is the solution for (d^2y)/(dt^2)+6(dy)/(dt)+9y=0 ?
The solution for (d^2y)/(dt^2)+6(dy)/(dt)+9y=0 is y=c_{1}e^{-3t}+c_{2}te^{-3t}