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

The solution for y^{'''}-3y^{''}-y^'+3y=e^{6x} is y=c_{1}e^{3x}+c_{2}e^{-x}+c_{3}e^x+1/105 e^{6x}

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

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

y = c_{1} e^{3 x} + c_{2} e^{- x} + c_{3} e^{x} + \frac{1}{105} e^{6 x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- x} + c_{3} e^{x} + \frac{1}{105} e^{6 x}

y = c_{1} e^{3 x} + c_{2} e^{- x} + c_{3} e^{x} + \frac{1}{105} e^{6 x}

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

y^{^{''}} - 11 y^{^{'}} + 28 y = 216 e^{t}

y^{^{''}} - 6 y^{^{'}} + 9 y = 4 e^{- 3 t}

y^{^{''}} + 5 y^{^{'}} + 6 y = sin (x)

y^{^{''}} - y^{^{'}} - 6 y = 70 cos (3 x)

What is the solution for y^{'''}-3y^{''}-y^'+3y=e^{6x} ?
The solution for y^{'''}-3y^{''}-y^'+3y=e^{6x} is y=c_{1}e^{3x}+c_{2}e^{-x}+c_{3}e^x+1/105 e^{6x}