What is the solution for y^{'''}-6y^{''}+11y^'-6y=-1 ?

The solution for y^{'''}-6y^{''}+11y^'-6y=-1 is y=c_{1}e^t+c_{2}e^{2t}+c_{3}e^{3t}+1/6

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y^{'''}-6y^{''}+11y^'-6y=-1

y^{^{'''}} - 6 y^{^{''}} + 11 y^{^{'}} - 6 y = - 1

y = c_{1} e^{t} + c_{2} e^{2 t} + c_{3} e^{3 t} + \frac{1}{6}

Solution steps

y^{'''} (t) - 6 y^{''} (t) + 11 y^{'} (t) - 6 y = - 1

Solve linear ODE:

y = c_{1} e^{t} + c_{2} e^{2 t} + c_{3} e^{3 t} + \frac{1}{6}

y = c_{1} e^{t} + c_{2} e^{2 t} + c_{3} e^{3 t} + \frac{1}{6}

What is the solution for y^{'''}-6y^{''}+11y^'-6y=-1 ?
The solution for y^{'''}-6y^{''}+11y^'-6y=-1 is y=c_{1}e^t+c_{2}e^{2t}+c_{3}e^{3t}+1/6