What is the solution for y^{''}+10y^'+16y=0,y(0)=1,y^'(0)=-12 ?

The solution for y^{''}+10y^'+16y=0,y(0)=1,y^'(0)=-12 is y=(1-5/3)e^{-2t}+5/3 e^{-8t}

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y^{''}+10y^'+16y=0,y(0)=1,y^'(0)=-12

y^{^{''}} + 10 y^{^{'}} + 16 y = 0, y (0) = 1, y^{^{'}} (0) = - 12

y = (1 - \frac{5}{3}) e^{- 2 t} + \frac{5}{3} e^{- 8 t}

Solution steps

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

Solve linear ODE:

y = (1 - \frac{5}{3}) e^{- 2 t} + \frac{5}{3} e^{- 8 t}

y = (1 - \frac{5}{3}) e^{- 2 t} + \frac{5}{3} e^{- 8 t}

y^{^{''}} + 9 π^{2} y = 0

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (- 1) = 2, y^{^{'}} (- 1) = 5

y^{^{''}} + 8 y^{^{'}} + 41 y = 0, y^{^{'}} (0) = 2, y (0) = 1

36 y^{^{''}} + 25 y = 0

2 y^{^{''}} - 17 y^{^{'}} - 9 y = 0, y (0) = 4, y^{^{'}} (0) = - 7

What is the solution for y^{''}+10y^'+16y=0,y(0)=1,y^'(0)=-12 ?
The solution for y^{''}+10y^'+16y=0,y(0)=1,y^'(0)=-12 is y=(1-5/3)e^{-2t}+5/3 e^{-8t}