What is the solution for y^{''}+9y^'+8y=0,y(0)=1,y^'(0)=0 ?

The solution for y^{''}+9y^'+8y=0,y(0)=1,y^'(0)=0 is y=(1+1/7)e^{-t}-1/7 e^{-8t}

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y^{''}+9y^'+8y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 9 y^{^{'}} + 8 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y = (1 + \frac{1}{7}) e^{- t} - \frac{1}{7} e^{- 8 t}

Solution steps

y^{''} (t) + 9 y^{'} (t) + 8 y = 0

Solve linear ODE:

y = (1 + \frac{1}{7}) e^{- t} - \frac{1}{7} e^{- 8 t}

y = (1 + \frac{1}{7}) e^{- t} - \frac{1}{7} e^{- 8 t}

\int_{1}^{\infty} x e^{- 9 x} d x

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What is the solution for y^{''}+9y^'+8y=0,y(0)=1,y^'(0)=0 ?
The solution for y^{''}+9y^'+8y=0,y(0)=1,y^'(0)=0 is y=(1+1/7)e^{-t}-1/7 e^{-8t}