What is the solution for y^{''}+6y^'+9y=0,y(0)=-5,y^'(0)=14 ?

The solution for y^{''}+6y^'+9y=0,y(0)=-5,y^'(0)=14 is y=-5e^{-3t}-e^{-3t}t

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y^{''}+6y^'+9y=0,y(0)=-5,y^'(0)=14

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = - 5, y^{^{'}} (0) = 14

y = - 5 e^{- 3 t} - e^{- 3 t} t

Solution steps

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

Solve linear ODE:

y = - 5 e^{- 3 t} - e^{- 3 t} t

y = - 5 e^{- 3 t} - e^{- 3 t} t

y^{^{''}} = y, y (0) = 0, y^{^{'}} (1) = 1

\frac{d ^{2} y}{d t ^{2}} - 11 \frac{d y}{d t} + 10 y = 0

y^{^{''}} - y^{^{'}} - 30 y = 0, y (0) = - 2, y^{^{'}} (0) = 21

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = - 4, y^{^{'}} (0) = 15

9 y^{^{''}} + 8 y^{^{'}} - 7 y = 0

What is the solution for y^{''}+6y^'+9y=0,y(0)=-5,y^'(0)=14 ?
The solution for y^{''}+6y^'+9y=0,y(0)=-5,y^'(0)=14 is y=-5e^{-3t}-e^{-3t}t