What is the solution for y^{'''}-3y^{''}+3y^'-y=x-7ex ?

The solution for y^{'''}-3y^{''}+3y^'-y=x-7ex is y=c_{1}e^x+c_{2}xe^x+c_{3}x^2e^x+(-1+7e)x+3(-1+7e)

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y^{'''}-3y^{''}+3y^'-y=x-7ex

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = x - 7 e x

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} x^{2} e^{x} + (- 1 + 7 e) x + 3 (- 1 + 7 e)

Solution steps

y^{'''} (x) - 3 y^{''} (x) + 3 y^{'} (x) - y = x - 7 e x

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} x^{2} e^{x} + (- 1 + 7 e) x + 3 (- 1 + 7 e)

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} x^{2} e^{x} + (- 1 + 7 e) x + 3 (- 1 + 7 e)

y^{^{''}} - 2 y^{^{'}} - 3 y = 8 e^{- t}

y^{^{''}} - y^{^{'}} + 4 y = x^{3} e^{2 x} + x e^{2 x}

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

9 y^{^{''}} + 6 y^{^{'}} + y = x^{2}

y^{^{''}} + 10 y^{^{'}} + 26 y = 2 e^{- 5 x} cos (x)

What is the solution for y^{'''}-3y^{''}+3y^'-y=x-7ex ?
The solution for y^{'''}-3y^{''}+3y^'-y=x-7ex is y=c_{1}e^x+c_{2}xe^x+c_{3}x^2e^x+(-1+7e)x+3(-1+7e)