What is the solution for y^{'''}+6y^{''}+9y^'=6x+2 ?

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

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y^{'''}+6y^{''}+9y^'=6x+2

y^{^{'''}} + 6 y^{^{''}} + 9 y^{^{'}} = 6 x + 2

y = c_{1} + c_{2} e^{- 3 x} + c_{3} x e^{- 3 x} + \frac{x ^{2}}{3} - \frac{2 x}{9}

Solution steps

y^{'''} (x) + 6 y^{''} (x) + 9 y^{'} (x) = 6 x + 2

Solve linear ODE:

y = c_{1} + c_{2} e^{- 3 x} + c_{3} x e^{- 3 x} + \frac{x ^{2}}{3} - \frac{2 x}{9}

y = c_{1} + c_{2} e^{- 3 x} + c_{3} x e^{- 3 x} + \frac{x ^{2}}{3} - \frac{2 x}{9}

y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = t^{3} e^{2 t} + 1

y^{^{''}} + 4 y = e^{3 x} + x sin (2 x)

y^{^{''}} + 3 y^{^{'}} + 2 y = \frac{1}{( 1 + e ^{x} )}

y^{^{'''}} - 9 y^{^{''}} + 108 y = e^{6 x}

y^{^{''}} - 36 y = cosh (6 x)

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