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

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

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

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

y = e^{- 3 t - 3} (5 + e^{3} c_{2}) + c_{2} e^{- 3 t} t

Solution steps

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

Solve linear ODE:

y = e^{- 3 t - 3} (5 + e^{3} c_{2}) + c_{2} e^{- 3 t} t

y = e^{- 3 t - 3} (5 + e^{3} c_{2}) + c_{2} e^{- 3 t} t

y^{^{''}} + 8 y^{^{'}} + 16 y = 0, y^{0} = 1, y^{^{'}} 0 = 0

y^{^{''}} - 2 π y^{^{'}} + π^{2} y = 0

y^{^{''}} - 2 y - 3 y = 0

4 y^{^{''}} + 16 y^{^{'}} + 25 y = 0

y^{^{''}} - 14 y^{^{'}} + 65 y = 0

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