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

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

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

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

y = (1 + \frac{1}{5}) e^{- t} - \frac{1}{5} e^{- 6 t}

Solution steps

y^{''} (t) + 7 y^{'} (t) + 6 y = 0

Solve linear ODE:

y = (1 + \frac{1}{5}) e^{- t} - \frac{1}{5} e^{- 6 t}

y = (1 + \frac{1}{5}) e^{- t} - \frac{1}{5} e^{- 6 t}

\int (\frac{9}{x} - \frac{2}{x ^{3}}) d x

\frac{d}{d x} (x e^{y^{2}})

\frac{d}{d x} (\frac{- x ^{2}}{2})

x \to \frac{c}{2 ^{+}} lim ([2 x - 4])

y^{^{''}} + y = 3

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