What is the solution for y^{''}+6y^'+9y=0,y(0)=-1,y^'(0)=1 ?

The solution for y^{''}+6y^'+9y=0,y(0)=-1,y^'(0)=1 is y=-e^{-3t}-2e^{-3t}t

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y^{''}+6y^'+9y=0,y(0)=-1,y^'(0)=1

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = - 1, y^{^{'}} (0) = 1

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

Solution steps

y^{''} (t) + 6 y^{'} (t) + 9 y = 0

Solve linear ODE:

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

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

y^{^{''}} + 4 y^{^{'}} + 68 y = 0, y (0) = 7

2 x^{^{''}} + 32 x = 0, x (0) = 0, x^{^{'}} (0) = 0

y^{^{''}} + y = 0, y (0) = 11, y (0) = 33

4 \frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} = 0

y^{^{'''}} + 2 y^{^{''}} - 11 y^{^{'}} - 52 y = 0

What is the solution for y^{''}+6y^'+9y=0,y(0)=-1,y^'(0)=1 ?
The solution for y^{''}+6y^'+9y=0,y(0)=-1,y^'(0)=1 is y=-e^{-3t}-2e^{-3t}t