What is the solution for y^{''}+6y^'+9y=0,y(0)=2,y^'(0)=-7 ?

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

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y^{''}+6y^'+9y=0,y(0)=2,y^'(0)=-7

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = - 7

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

Solution steps

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

Solve linear ODE:

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

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

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\int \frac{3}{x} + x^{3} d x

\frac{\partial}{\partial x} (4 y cos (x))

\frac{d x}{d t} = sin (3 t) cos (3 t)

x^{3} - 17 x^{2} + 63 x + 6

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