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}

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}