What is the solution for y^{''}+6y^'+9y=0,y(0)=-4,y^'(0)=15 ?

The solution for y^{''}+6y^'+9y=0,y(0)=-4,y^'(0)=15 is y=-4e^{-3t}+3e^{-3t}t

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

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

y = - 4 e^{- 3 t} + 3 e^{- 3 t} t

Solution steps

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

Solve linear ODE:

y = - 4 e^{- 3 t} + 3 e^{- 3 t} t

y = - 4 e^{- 3 t} + 3 e^{- 3 t} t

What is the solution for y^{''}+6y^'+9y=0,y(0)=-4,y^'(0)=15 ?
The solution for y^{''}+6y^'+9y=0,y(0)=-4,y^'(0)=15 is y=-4e^{-3t}+3e^{-3t}t