What is the solution for y^{''}+6y^'+9y=0,y(0)=2,y^'(0)=-25/3 ?

The solution for y^{''}+6y^'+9y=0,y(0)=2,y^'(0)=-25/3 is y=2e^{-3t}-(7e^{-3t}t)/3

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y^{''}+6y^'+9y=0,y(0)=2,y^'(0)=-25/3

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = - \frac{25}{3}

y = 2 e^{- 3 t} - \frac{7 e ^{- 3 t} t}{3}

Solution steps

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

Solve linear ODE:

y = 2 e^{- 3 t} - \frac{7 e ^{- 3 t} t}{3}

y = 2 e^{- 3 t} - \frac{7 e ^{- 3 t} t}{3}

\int \frac{( x + 2 )}{x} d x

\frac{d}{d x} (a^{x} ln (x))

11 x - 4 y x^{2} + 1 \frac{d y}{d x} = 0

f (t) = 4 t^{2} - t

x \to 1 lim (x^{2} - x)

What is the solution for y^{''}+6y^'+9y=0,y(0)=2,y^'(0)=-25/3 ?
The solution for y^{''}+6y^'+9y=0,y(0)=2,y^'(0)=-25/3 is y=2e^{-3t}-(7e^{-3t}t)/3