What is the solution for y^{''}+8y^'+7y=0,y(0)=6,y^'(0)=-1 ?

The solution for y^{''}+8y^'+7y=0,y(0)=6,y^'(0)=-1 is y=(6+5/6)e^{-t}-5/6 e^{-7t}

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y^{''}+8y^'+7y=0,y(0)=6,y^'(0)=-1

y^{^{''}} + 8 y^{^{'}} + 7 y = 0, y (0) = 6, y^{^{'}} (0) = - 1

y = (6 + \frac{5}{6}) e^{- t} - \frac{5}{6} e^{- 7 t}

Solution steps

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

Solve linear ODE:

y = (6 + \frac{5}{6}) e^{- t} - \frac{5}{6} e^{- 7 t}

y = (6 + \frac{5}{6}) e^{- t} - \frac{5}{6} e^{- 7 t}

\frac{d ^{2}}{d x ^{2}} (x^{4} - 6 x^{3})

\frac{\partial}{\partial x} (\frac{7 x}{x ^{2} + y ^{2}})

sin (6 (t - \frac{5 π}{6}))

\frac{1}{s ( 1 + s )}

y = x, y = \frac{x}{3}, y = 2

What is the solution for y^{''}+8y^'+7y=0,y(0)=6,y^'(0)=-1 ?
The solution for y^{''}+8y^'+7y=0,y(0)=6,y^'(0)=-1 is y=(6+5/6)e^{-t}-5/6 e^{-7t}