(D^4-2D^3+D)y=x^4+3x+1

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Solution for (D^4-2D^3+D)y=x^4+3x+1 equation: 


Simplifying
(D4 + -2D3 + D) * y = x4 + 3x + 1

Reorder the terms:
(D + -2D3 + D4) * y = x4 + 3x + 1

Reorder the terms for easier multiplication:
y(D + -2D3 + D4) = x4 + 3x + 1
(D * y + -2D3 * y + D4 * y) = x4 + 3x + 1
(yD + -2yD3 + yD4) = x4 + 3x + 1

Reorder the terms:
yD + -2yD3 + yD4 = 1 + 3x + x4

Solving
yD + -2yD3 + yD4 = 1 + 3x + x4

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Reorder the terms:
-1 + -3x + -1x4 + yD + -2yD3 + yD4 = 1 + 3x + x4 + -1 + -3x + -1x4

Reorder the terms:
-1 + -3x + -1x4 + yD + -2yD3 + yD4 = 1 + -1 + 3x + -3x + x4 + -1x4

Combine like terms: 1 + -1 = 0
-1 + -3x + -1x4 + yD + -2yD3 + yD4 = 0 + 3x + -3x + x4 + -1x4
-1 + -3x + -1x4 + yD + -2yD3 + yD4 = 3x + -3x + x4 + -1x4

Combine like terms: 3x + -3x = 0
-1 + -3x + -1x4 + yD + -2yD3 + yD4 = 0 + x4 + -1x4
-1 + -3x + -1x4 + yD + -2yD3 + yD4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-1 + -3x + -1x4 + yD + -2yD3 + yD4 = 0

The solution to this equation could not be determined.

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