What is the solution for y^{''}+6y^'+9y=18t^2+24t+4 ?

The solution for y^{''}+6y^'+9y=18t^2+24t+4 is y=c_{1}e^{-3t}+c_{2}te^{-3t}+2t^2

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y^{''}+6y^'+9y=18t^2+24t+4

y^{^{''}} + 6 y^{^{'}} + 9 y = 18 t^{2} + 24 t + 4

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

Solution steps

y^{''} (t) + 6 y^{'} (t) + 9 y = 18 t^{2} + 24 t + 4

Solve linear ODE:

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

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

What is the solution for y^{''}+6y^'+9y=18t^2+24t+4 ?
The solution for y^{''}+6y^'+9y=18t^2+24t+4 is y=c_{1}e^{-3t}+c_{2}te^{-3t}+2t^2