What is the solution for (d^2y)/(dt^2)+18(dy)/(dt)+81y=0 ?

The solution for (d^2y)/(dt^2)+18(dy)/(dt)+81y=0 is y=c_{1}e^{-9t}+c_{2}te^{-9t}

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(d^2y)/(dt^2)+18(dy)/(dt)+81y=0

\frac{d ^{2} y}{d t ^{2}} + 18 \frac{d y}{d t} + 81 y = 0

y = c_{1} e^{- 9 t} + c_{2} t e^{- 9 t}

Solution steps

\frac{d ^{2} y}{d t ^{2}} + 18 \frac{d y}{d t} + 81 y = 0

Solve linear ODE:

y = c_{1} e^{- 9 t} + c_{2} t e^{- 9 t}

y = c_{1} e^{- 9 t} + c_{2} t e^{- 9 t}

What is the solution for (d^2y)/(dt^2)+18(dy)/(dt)+81y=0 ?
The solution for (d^2y)/(dt^2)+18(dy)/(dt)+81y=0 is y=c_{1}e^{-9t}+c_{2}te^{-9t}