What is the solution for y^{''}+2y^'+y=21e^{-t} ?

The solution for y^{''}+2y^'+y=21e^{-t} is y=c_{1}e^{-t}+c_{2}te^{-t}+(21e^{-t}t^2)/2

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y^{''}+2y^'+y=21e^{-t}

y^{^{''}} + 2 y^{^{'}} + y = 21 e^{- t}

y = c_{1} e^{- t} + c_{2} t e^{- t} + \frac{21 e ^{- t} t ^{2}}{2}

Solution steps

y^{''} (t) + 2 y^{'} (t) + y = 21 e^{- t}

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} t e^{- t} + \frac{21 e ^{- t} t ^{2}}{2}

y = c_{1} e^{- t} + c_{2} t e^{- t} + \frac{21 e ^{- t} t ^{2}}{2}

y^{^{''}} - 2 y^{^{'}} + y = 8 e^{x} - \frac{1}{6} x^{3} + 3 x

y^{^{''}} + 9 y^{^{'}} - 22 y = e^{- 3 x}

y^{^{''}} + y^{^{'}} = 5

3 y^{^{''}} + 4 y + 2 = 0

y^{^{''}} + 5 y^{^{'}} + 6 y = 2 e^{- t}

What is the solution for y^{''}+2y^'+y=21e^{-t} ?
The solution for y^{''}+2y^'+y=21e^{-t} is y=c_{1}e^{-t}+c_{2}te^{-t}+(21e^{-t}t^2)/2