What is the solution for y^{''}+8y^'+7y=0,y(0)=1,y^'(0)=0 ?

The solution for y^{''}+8y^'+7y=0,y(0)=1,y^'(0)=0 is y=(1+1/6)e^{-t}-1/6 e^{-7t}

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y^{''}+8y^'+7y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 8 y^{^{'}} + 7 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y = (1 + \frac{1}{6}) e^{- t} - \frac{1}{6} e^{- 7 t}

Solution steps

y^{''} (t) + 8 y^{'} (t) + 7 y = 0

Solve linear ODE:

y = (1 + \frac{1}{6}) e^{- t} - \frac{1}{6} e^{- 7 t}

y = (1 + \frac{1}{6}) e^{- t} - \frac{1}{6} e^{- 7 t}

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

x^{^{'''}} - 12 x^{^{''}} + 48 x^{^{'}} - 64 x = 0

y^{^{''}} = 4 y^{^{'}} - 3 y

(D^{2} + 3 D - 10) y = 0

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

What is the solution for y^{''}+8y^'+7y=0,y(0)=1,y^'(0)=0 ?
The solution for y^{''}+8y^'+7y=0,y(0)=1,y^'(0)=0 is y=(1+1/6)e^{-t}-1/6 e^{-7t}