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

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

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

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

y = (1 - c_{2}) e^{- t} + c_{2} e^{- 4 t}

Solution steps

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

Solve linear ODE:

y = (1 - c_{2}) e^{- t} + c_{2} e^{- 4 t}

y = (1 - c_{2}) e^{- t} + c_{2} e^{- 4 t}

y^{^{''}} - y^{^{'}} - 2 y = 0, y (0) = 8

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

y^{^{''}} - y^{^{'}} - 2 y = 0, y (0) = 5

36 y^{^{''}} - 36 y^{^{'}} + 13 y = 0

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

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