What is the solution for y^{''}+6y^'+8y=0,y(0)=2,y^'(0)=-6 ?

The solution for y^{''}+6y^'+8y=0,y(0)=2,y^'(0)=-6 is y=e^{-2t}+e^{-4t}

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y^{''}+6y^'+8y=0,y(0)=2,y^'(0)=-6

y^{^{''}} + 6 y^{^{'}} + 8 y = 0, y (0) = 2, y^{^{'}} (0) = - 6

y = e^{- 2 t} + e^{- 4 t}

Solution steps

y^{''} (t) + 6 y^{'} (t) + 8 y = 0

Solve linear ODE:

y = e^{- 2 t} + e^{- 4 t}

y = e^{- 2 t} + e^{- 4 t}

y^{^{'}} + 2 y^{^{''}} + y = 0

y^{^{''}} - (8) y^{^{'}} + α y = 0, y (0) = 1, y^{^{'}} (0) = - 73

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

9 y^{^{''}} + 18 y^{^{'}} + 13 y = 0

q^{^{''}} + 20 q^{^{'}} + 100 q = 0

What is the solution for y^{''}+6y^'+8y=0,y(0)=2,y^'(0)=-6 ?
The solution for y^{''}+6y^'+8y=0,y(0)=2,y^'(0)=-6 is y=e^{-2t}+e^{-4t}