What is the solution for y^{'''}-3y^{''}+3y^'-y=x-8ex ?

The solution for y^{'''}-3y^{''}+3y^'-y=x-8ex is y=c_{1}e^x+c_{2}xe^x+c_{3}x^2e^x+(-1+8e)x+3(-1+8e)

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y^{'''}-3y^{''}+3y^'-y=x-8ex

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = x - 8 e x

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} x^{2} e^{x} + (- 1 + 8 e) x + 3 (- 1 + 8 e)

Solution steps

y^{'''} (x) - 3 y^{''} (x) + 3 y^{'} (x) - y = x - 8 e x

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} x^{2} e^{x} + (- 1 + 8 e) x + 3 (- 1 + 8 e)

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} x^{2} e^{x} + (- 1 + 8 e) x + 3 (- 1 + 8 e)

y^{^{''}} - 36 y^{^{'}} = - 42 e^{- 5 t}, y (0) = 7, y^{^{'}} (0) = 0

2 \frac{d ^{2} y}{d t ^{2}} + 20 \frac{d y}{d t} + 50 = 8 \cdot (t)

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

x^{^{''}} - 3 x^{^{'}} + 2 x = 2 sin (t) - 6 cos (t)

x^{^{''}} + 8 x^{^{'}} + 16 x = 10 sin (4 t)

What is the solution for y^{'''}-3y^{''}+3y^'-y=x-8ex ?
The solution for y^{'''}-3y^{''}+3y^'-y=x-8ex is y=c_{1}e^x+c_{2}xe^x+c_{3}x^2e^x+(-1+8e)x+3(-1+8e)