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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 3 y^{^{'}} - 4 y = 0, y (0) = 1, y^{^{'}} (0) = 3

\frac{d ^{4} y}{d x ^{4}} - 7 \frac{d ^{2} y}{d x ^{2}} - 18 y = 0

\frac{d ^{2} y}{d x ^{2}} - 10 \frac{d y}{d x} + 25 y = 0

(\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 20 y)^{2} = 0

y^{^{''}} - 9 y^{^{'}} - 22 y = 0

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