What is the solution for y^{''}+2y^'+y=0,y(1)=6 ?

The solution for y^{''}+2y^'+y=0,y(1)=6 is y=(6e-c_{2})e^{-t}+c_{2}te^{-t}

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y^{''}+2y^'+y=0,y(1)=6

y^{^{''}} + 2 y^{^{'}} + y = 0, y (1) = 6

y = (6 e - c_{2}) e^{- t} + c_{2} t e^{- t}

Solution steps

y^{''} (t) + 2 y^{'} (t) + y = 0

Solve linear ODE:

y = (6 e - c_{2}) e^{- t} + c_{2} t e^{- t}

y = (6 e - c_{2}) e^{- t} + c_{2} t e^{- t}

What is the solution for y^{''}+2y^'+y=0,y(1)=6 ?
The solution for y^{''}+2y^'+y=0,y(1)=6 is y=(6e-c_{2})e^{-t}+c_{2}te^{-t}