What is the solution for y^{''}+10y^'+16y=0,y(0)=1,y^'(0)=0 ?

The solution for y^{''}+10y^'+16y=0,y(0)=1,y^'(0)=0 is y=(1+1/3)e^{-2t}-1/3 e^{-8t}

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y^{''}+10y^'+16y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 10 y^{^{'}} + 16 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y = (1 + \frac{1}{3}) e^{- 2 t} - \frac{1}{3} e^{- 8 t}

Solution steps

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

Solve linear ODE:

y = (1 + \frac{1}{3}) e^{- 2 t} - \frac{1}{3} e^{- 8 t}

y = (1 + \frac{1}{3}) e^{- 2 t} - \frac{1}{3} e^{- 8 t}

y^{^{''}} + k y^{^{'}} + 8 y = 0, y (0) = e^{2 x} sin (2 x)

y^{^{''}} - 10 y = 0

\frac{d ^{2} y}{d x ^{2}} + 25 y = 0

y^{^{''}} - y^{^{'}} - 20 y = 0, y (0) = 4, y^{^{'}} (0) = 29

y^{^{''}} - 8 y^{^{'}} + 2 y = 0

What is the solution for y^{''}+10y^'+16y=0,y(0)=1,y^'(0)=0 ?
The solution for y^{''}+10y^'+16y=0,y(0)=1,y^'(0)=0 is y=(1+1/3)e^{-2t}-1/3 e^{-8t}