What is the solution for y^{''}+6y^'+9y=27+e^{-3x} ?

The solution for y^{''}+6y^'+9y=27+e^{-3x} is y=c_{1}e^{-3x}+c_{2}xe^{-3x}+3+(e^{-3x}x^2)/2

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y^{''}+6y^'+9y=27+e^{-3x}

y^{^{''}} + 6 y^{^{'}} + 9 y = 27 + e^{- 3 x}

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

Solution steps

y^{''} (x) + 6 y^{'} (x) + 9 y = 27 + e^{- 3 x}

Solve linear ODE:

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

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

\int e^{3 l n (4 x - 5)} d x

\int t sin^{2} (t) d t

f (x) = 5 - 3 x

y^{^{'}} - 1 = y^{2}

\frac{2}{s ( s ^{2} + 2 s + 2 )}

What is the solution for y^{''}+6y^'+9y=27+e^{-3x} ?
The solution for y^{''}+6y^'+9y=27+e^{-3x} is y=c_{1}e^{-3x}+c_{2}xe^{-3x}+3+(e^{-3x}x^2)/2