What is the solution for y^{''}+6y^'+9y=0,y(0)=-5/3 ?

The solution for y^{''}+6y^'+9y=0,y(0)=-5/3 is y=-5/3 e^{-3t}+c_{2}e^{-3t}t

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y^{''}+6y^'+9y=0,y(0)=-5/3

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = - \frac{5}{3}

y = - \frac{5}{3} e^{- 3 t} + c_{2} e^{- 3 t} t

Solution steps

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

Solve linear ODE:

y = - \frac{5}{3} e^{- 3 t} + c_{2} e^{- 3 t} t

y = - \frac{5}{3} e^{- 3 t} + c_{2} e^{- 3 t} t

x^{^{''}} + 5 x^{^{'}} + 3 x = 0, x (0) = 5, x^{^{'}} (0) = 7

y^{^{''}} - 22 y^{^{'}} + 121 y = 0, y (0) = 0, y^{^{'}} (0) = 5

y^{^{''}} + 9 y^{^{'}} + 14 y = 0, y (0) = 0, y^{^{'}} (0) = - 1

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = 2, y^{^{'}} (0) = - 9

y^{^{''}} - y^{^{'}} - 12 y = 0, y (0) = 2, y^{^{'}} (0) = - 3

What is the solution for y^{''}+6y^'+9y=0,y(0)=-5/3 ?
The solution for y^{''}+6y^'+9y=0,y(0)=-5/3 is y=-5/3 e^{-3t}+c_{2}e^{-3t}t