What is the solution for y^{''}+10y^'+16y=0,y(0)=0,y^'(0)=-6 ?

The solution for y^{''}+10y^'+16y=0,y(0)=0,y^'(0)=-6 is y=-e^{-2t}+e^{-8t}

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y^{''}+10y^'+16y=0,y(0)=0,y^'(0)=-6

y^{^{''}} + 10 y^{^{'}} + 16 y = 0, y (0) = 0, y^{^{'}} (0) = - 6

y = - e^{- 2 t} + e^{- 8 t}

Solution steps

y^{''} (t) + 10 y^{'} (t) + 16 y = 0

Solve linear ODE:

y = - e^{- 2 t} + e^{- 8 t}

y = - e^{- 2 t} + e^{- 8 t}

y^{^{''}} = \frac{y}{4}

y^{^{''}} - 4 y^{^{'}} + 8 y = 0, y^{^{'}} (0) = 2, y (0) = 0

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

y^{^{''}} + 4 y^{1} - y = 0

y^{^{''}} + π^{2} \cdot y = 0

What is the solution for y^{''}+10y^'+16y=0,y(0)=0,y^'(0)=-6 ?
The solution for y^{''}+10y^'+16y=0,y(0)=0,y^'(0)=-6 is y=-e^{-2t}+e^{-8t}