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

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

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

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

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

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

x^{^{''}} + 3 x^{^{'}} - 4 x = 0

y^{^{''}} + 16 y^{^{'}} + 73 y = 0, y (0) = 4

y^{^{''}} + 6 y^{^{'}} + 10 y = 0, y (\frac{π}{2}) = 0, y^{^{'}} (\frac{π}{2}) = 9

y^{^{''}} + 6 y^{^{'}} + 10 y = 0, y (\frac{π}{2}) = 0, y^{^{'}} (\frac{π}{2}) = 2

y^{^{''}} + \frac{y}{4} = 0

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