What is the solution for y^{''}+2y^'+y=6e^{-t} ?

The solution for y^{''}+2y^'+y=6e^{-t} is y=c_{1}e^{-t}+c_{2}te^{-t}+3t^2e^{-t}

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y^{''}+2y^'+y=6e^{-t}

y^{^{''}} + 2 y^{^{'}} + y = 6 e^{- t}

y = c_{1} e^{- t} + c_{2} t e^{- t} + 3 t^{2} e^{- t}

Solution steps

y^{''} (t) + 2 y^{'} (t) + y = 6 e^{- t}

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} t e^{- t} + 3 t^{2} e^{- t}

y = c_{1} e^{- t} + c_{2} t e^{- t} + 3 t^{2} e^{- t}

\int \frac{1}{4} e^{- 2 x} d x

f (x) = 4 x^{2} - 5 x + 2

ln (\frac{2}{2 - x})

\frac{d}{d x} (x^{2} e^{- \frac{1}{x}})

\frac{1}{1 + x ^{2}}, x = 2

What is the solution for y^{''}+2y^'+y=6e^{-t} ?
The solution for y^{''}+2y^'+y=6e^{-t} is y=c_{1}e^{-t}+c_{2}te^{-t}+3t^2e^{-t}