What is the solution for y^{''}+6y^'+9y=0,y(0)=2,y^'(0)=0 ?

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

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y^{''}+6y^'+9y=0,y(0)=2,y^'(0)=0

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = 0

y = 2 e^{- 3 t} + 6 t e^{- 3 t}

Solution steps

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

Solve linear ODE:

y = 2 e^{- 3 t} + 6 t e^{- 3 t}

y = 2 e^{- 3 t} + 6 t e^{- 3 t}

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