What is the solution for y^{''}+6y^'+9y=6t^2e^{-3t} ?

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

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y^{''}+6y^'+9y=6t^2e^{-3t}

y^{^{''}} + 6 y^{^{'}} + 9 y = 6 t^{2} e^{- 3 t}

y = c_{1} e^{- 3 t} + c_{2} t e^{- 3 t} + \frac{e ^{- 3 t} t ^{4}}{2}

Solution steps

y^{''} (t) + 6 y^{'} (t) + 9 y = 6 t^{2} e^{- 3 t}

Solve linear ODE:

y = c_{1} e^{- 3 t} + c_{2} t e^{- 3 t} + \frac{e ^{- 3 t} t ^{4}}{2}

y = c_{1} e^{- 3 t} + c_{2} t e^{- 3 t} + \frac{e ^{- 3 t} t ^{4}}{2}

\frac{\partial}{\partial x} (x e^{x^{2} - y})

x \to 0 lim (\frac{9 e ^{x} - 9}{x})

f (x) = 4 sec (4 x)

\int (6 x^{5} + 7) x^{6} + 7 x d x

lo g_{e} (sec (\frac{1}{5 x}))

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