What is the solution for y^{''}+10y^'+16y=0,y(0)=9,y^'(0)=-60 ?

The solution for y^{''}+10y^'+16y=0,y(0)=9,y^'(0)=-60 is y=2e^{-2t}+7e^{-8t}

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y^{''}+10y^'+16y=0,y(0)=9,y^'(0)=-60

y^{^{''}} + 10 y^{^{'}} + 16 y = 0, y (0) = 9, y^{^{'}} (0) = - 60

y = 2 e^{- 2 t} + 7 e^{- 8 t}

Solution steps

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

Solve linear ODE:

y = 2 e^{- 2 t} + 7 e^{- 8 t}

y = 2 e^{- 2 t} + 7 e^{- 8 t}

y^{^{'''}} - 7 y^{^{''}} + 12 y^{^{'}} = 0

x^{^{''}} + 2 x^{^{'}} - 8 x = 0, x^{^{'}} (0) = 22, x (0) = - 1

\frac{d ^{2} x}{d t ^{2}} - 4 \frac{d x}{d t} + 5 x = 0

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

4 y^{^{''}} + 24 y^{^{'}} + 37 y = 0, y (π) = 1

What is the solution for y^{''}+10y^'+16y=0,y(0)=9,y^'(0)=-60 ?
The solution for y^{''}+10y^'+16y=0,y(0)=9,y^'(0)=-60 is y=2e^{-2t}+7e^{-8t}