What is the solution for y^{''}+6y^'+8y=0,y(0)=0,y^'(0)=-5 ?

The solution for y^{''}+6y^'+8y=0,y(0)=0,y^'(0)=-5 is y=-5/2 e^{-2t}+5/2 e^{-4t}

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y^{''}+6y^'+8y=0,y(0)=0,y^'(0)=-5

y^{^{''}} + 6 y^{^{'}} + 8 y = 0, y (0) = 0, y^{^{'}} (0) = - 5

y = - \frac{5}{2} e^{- 2 t} + \frac{5}{2} e^{- 4 t}

Solution steps

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

Solve linear ODE:

y = - \frac{5}{2} e^{- 2 t} + \frac{5}{2} e^{- 4 t}

y = - \frac{5}{2} e^{- 2 t} + \frac{5}{2} e^{- 4 t}

y^{^{''}} - y^{^{'}} - 72 y^{^{'}} = 0

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

\frac{y ^{^{''}}}{8} + 30 y^{^{'}} + 500 y = 0

y^{^{''}} - 36 \cdot y = 0

y^{^{''}} - 23 y^{^{'}} + 112 y = 0, y (0) = 3, y^{^{'}} (0) = 48

What is the solution for y^{''}+6y^'+8y=0,y(0)=0,y^'(0)=-5 ?
The solution for y^{''}+6y^'+8y=0,y(0)=0,y^'(0)=-5 is y=-5/2 e^{-2t}+5/2 e^{-4t}