What is the solution for y^{''}+5y^'+4y=0,y^'(0)=1,y(0)=1 ?

The solution for y^{''}+5y^'+4y=0,y^'(0)=1,y(0)=1 is y=(-1+8/3)e^{-t}-2/3 e^{-4t}

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

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

y = (- 1 + \frac{8}{3}) e^{- t} - \frac{2}{3} e^{- 4 t}

Solution steps

y^{''} (t) + 5 y^{'} (t) + 4 y = 0

Solve linear ODE:

y = (- 1 + \frac{8}{3}) e^{- t} - \frac{2}{3} e^{- 4 t}

y = (- 1 + \frac{8}{3}) e^{- t} - \frac{2}{3} e^{- 4 t}

y^{^{''}} + 1000 y^{^{'}} + 250000 y = 0

y^{^{''}} + 9 y = 0, y (0) = 5, y^{^{'}} (0) = - 7

2 y - y^{^{''}} = 0

2 y = 3 y^{^{''}}

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = 1

What is the solution for y^{''}+5y^'+4y=0,y^'(0)=1,y(0)=1 ?
The solution for y^{''}+5y^'+4y=0,y^'(0)=1,y(0)=1 is y=(-1+8/3)e^{-t}-2/3 e^{-4t}