What is the solution for y^{'''}-3y^{''}+3y^'-y=x-5ex ?

The solution for y^{'''}-3y^{''}+3y^'-y=x-5ex is y=c_{1}e^x+c_{2}xe^x+c_{3}x^2e^x+(-1+5e)x+3(-1+5e)

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y^{'''}-3y^{''}+3y^'-y=x-5ex

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = x - 5 e x

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} x^{2} e^{x} + (- 1 + 5 e) x + 3 (- 1 + 5 e)

Solution steps

y^{'''} (x) - 3 y^{''} (x) + 3 y^{'} (x) - y = x - 5 e x

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} x^{2} e^{x} + (- 1 + 5 e) x + 3 (- 1 + 5 e)

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} x^{2} e^{x} + (- 1 + 5 e) x + 3 (- 1 + 5 e)

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

y^{^{''}} - 3 y^{^{'}} + 2 y = - e^{t} + 2 e^{2 t}

y^{^{''}} + y = 3 t^{2}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 4 y = cos (4 t)

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

What is the solution for y^{'''}-3y^{''}+3y^'-y=x-5ex ?
The solution for y^{'''}-3y^{''}+3y^'-y=x-5ex is y=c_{1}e^x+c_{2}xe^x+c_{3}x^2e^x+(-1+5e)x+3(-1+5e)