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

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

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

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

y = c_{1} e^{x} + c_{2} e^{2 x} + c_{3} e^{3 x} - \frac{x}{2} - \frac{11}{12}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{2 x} + c_{3} e^{3 x} - \frac{x}{2} - \frac{11}{12}

y = c_{1} e^{x} + c_{2} e^{2 x} + c_{3} e^{3 x} - \frac{x}{2} - \frac{11}{12}

(D^{2} - D) y = e^{x} sin (x)

(D^{3} + 2 D^{2} - 5 D - 6) y = e^{- 3 x}

y^{^{''}} + 4 y^{^{'}} + 4 y = sin (2 t)

y^{^{''}} + 16 y = 17 sec^{2} (4 t)

y^{^{''}} - y = t, y^{^{'}} (0) = 1

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