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

The solution for y^{''}+2y^'+y=t^2-6 is y=c_{1}e^{-t}+c_{2}te^{-t}+t^2-4t

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

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

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

Solution steps

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

Solve linear ODE:

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

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

What is the solution for y^{''}+2y^'+y=t^2-6 ?
The solution for y^{''}+2y^'+y=t^2-6 is y=c_{1}e^{-t}+c_{2}te^{-t}+t^2-4t