What is the solution for y^{''}+5y^'+6y=0,y(0)=1,y^'(0)=-3 ?

The solution for y^{''}+5y^'+6y=0,y(0)=1,y^'(0)=-3 is y=e^{-3t}

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y^{''}+5y^'+6y=0,y(0)=1,y^'(0)=-3

y^{^{''}} + 5 y^{^{'}} + 6 y = 0, y (0) = 1, y^{^{'}} (0) = - 3

y = e^{- 3 t}

Solution steps

y^{''} (t) + 5 y^{'} (t) + 6 y = 0

Solve linear ODE:

y = e^{- 3 t}

y = e^{- 3 t}

(d^{4} - 16) y = 0

y^{^{''}} - \frac{2}{3} y^{^{'}} + \frac{1}{9} y = 0

2 y^{^{''}} + 2 y^{^{'}} + 8 y = 0, y (0) = 5, y^{^{'}} (0) = 0

y^{^{''}} - 2 y^{^{'}} + y = 0, y (0) = 1, y^{^{'}} (0) = 3

y^{^{'}} = 4 y^{^{''}}

What is the solution for y^{''}+5y^'+6y=0,y(0)=1,y^'(0)=-3 ?
The solution for y^{''}+5y^'+6y=0,y(0)=1,y^'(0)=-3 is y=e^{-3t}