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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 4 y = - 7 e^{2 x} + x

y^{^{''}} - 2 y^{^{'}} + 5 y = 1 + t

y^{^{''}} + y^{^{'}} = cos (2 t)

y^{^{''}} + 16 y = 8 e^{4 t} + 8 sin (2 t)

y^{^{''}} - 6 y^{^{'}} + 15 y = 2 sin (3 t)

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