What is the solution for y^{'''}+6y^{''}+11y^'+6y=3+3x ?

The solution for y^{'''}+6y^{''}+11y^'+6y=3+3x is y=c_{1}e^{-x}+c_{2}e^{-2x}+c_{3}e^{-3x}+x/2-5/12

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y^{'''}+6y^{''}+11y^'+6y=3+3x

y^{^{'''}} + 6 y^{^{''}} + 11 y^{^{'}} + 6 y = 3 + 3 x

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + c_{3} e^{- 3 x} + \frac{x}{2} - \frac{5}{12}

Solution steps

y^{'''} (x) + 6 y^{''} (x) + 11 y^{'} (x) + 6 y = 3 + 3 x

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + c_{3} e^{- 3 x} + \frac{x}{2} - \frac{5}{12}

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + c_{3} e^{- 3 x} + \frac{x}{2} - \frac{5}{12}

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

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

(D^{2} - 3 D + 2) y = cos (3 x)

2 y^{^{''}} + y = - e^{3} + e^{2 x}

y^{^{'''}} + y^{^{''}} = 6

What is the solution for y^{'''}+6y^{''}+11y^'+6y=3+3x ?
The solution for y^{'''}+6y^{''}+11y^'+6y=3+3x is y=c_{1}e^{-x}+c_{2}e^{-2x}+c_{3}e^{-3x}+x/2-5/12