What is the solution for y^{''}+6y^'+9y=0,y(0)=4,y^'(0)=1 ?

The solution for y^{''}+6y^'+9y=0,y(0)=4,y^'(0)=1 is y=4e^{-3t}+13te^{-3t}

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y^{''}+6y^'+9y=0,y(0)=4,y^'(0)=1

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = 4, y^{^{'}} (0) = 1

y = 4 e^{- 3 t} + 13 t e^{- 3 t}

Solution steps

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

Solve linear ODE:

y = 4 e^{- 3 t} + 13 t e^{- 3 t}

y = 4 e^{- 3 t} + 13 t e^{- 3 t}

What is the solution for y^{''}+6y^'+9y=0,y(0)=4,y^'(0)=1 ?
The solution for y^{''}+6y^'+9y=0,y(0)=4,y^'(0)=1 is y=4e^{-3t}+13te^{-3t}