What is the solution for y^{''}+4y^'+4y=12te^{-2t}+4t ?

The solution for y^{''}+4y^'+4y=12te^{-2t}+4t is y=c_{1}e^{-2t}+c_{2}te^{-2t}+2e^{-2t}t^3+t-1

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y^{''}+4y^'+4y=12te^{-2t}+4t

y^{^{''}} + 4 y^{^{'}} + 4 y = 12 t e^{- 2 t} + 4 t

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

Solution steps

y^{''} (t) + 4 y^{'} (t) + 4 y = 12 t e^{- 2 t} + 4 t

Solve linear ODE:

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

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

(x + 2)^{2} + (y - 3)^{2} = 37, (- 1, 9)

\int tan (4 x) sec^{2} (4 x) d x

x^{2} - e^{y^{2}}

y = arctan (e^{x})

\int 3 x^{2} - 6 x d x

What is the solution for y^{''}+4y^'+4y=12te^{-2t}+4t ?
The solution for y^{''}+4y^'+4y=12te^{-2t}+4t is y=c_{1}e^{-2t}+c_{2}te^{-2t}+2e^{-2t}t^3+t-1