What is the solution for y^{''}+6y^'+9y=0,y(0)=1,y^'(0)=-5 ?

The solution for y^{''}+6y^'+9y=0,y(0)=1,y^'(0)=-5 is y=e^{-3t}-2e^{-3t}t

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y^{''}+6y^'+9y=0,y(0)=1,y^'(0)=-5

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = - 5

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^{^{''}} + 2 y^{^{'}} + 10 y = 0, y (0) = 3, y^{^{'}} (0) = - 2

y^{^{''}} + 3 \cdot y^{^{'}} + 2 \cdot y = 0, y (0) = 1, y^{^{'}} (0) = 1

3 y^{^{''}} + 24 y^{^{'}} + 48 y = 0, y (0) = 8, y^{^{'}} (0) = - 33

y^{^{''}} - 4 y^{^{'}} + 29 y = 0, y (0) = 6, y^{^{'}} (0) = - 3

6 y^{^{''}} - 13 y^{^{'}} + 6 y = 0

What is the solution for y^{''}+6y^'+9y=0,y(0)=1,y^'(0)=-5 ?
The solution for y^{''}+6y^'+9y=0,y(0)=1,y^'(0)=-5 is y=e^{-3t}-2e^{-3t}t