(D^3-3D^2-D+3)y=0

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Solution for (D^3-3D^2-D+3)y=0 equation:


Simplifying
(D3 + -3D2 + -1D + 3) * y = 0

Reorder the terms:
(3 + -1D + -3D2 + D3) * y = 0

Reorder the terms for easier multiplication:
y(3 + -1D + -3D2 + D3) = 0
(3 * y + -1D * y + -3D2 * y + D3 * y) = 0
(3y + -1yD + -3yD2 + yD3) = 0

Solving
3y + -1yD + -3yD2 + yD3 = 0

Solving for variable 'y'.

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

Factor out the Greatest Common Factor (GCF), 'y'.
y(3 + -1D + -3D2 + D3) = 0

Subproblem 1

Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0

Subproblem 2

Set the factor '(3 + -1D + -3D2 + D3)' equal to zero and attempt to solve: Simplifying 3 + -1D + -3D2 + D3 = 0 Solving 3 + -1D + -3D2 + D3 = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -1D + -3D2 + -3 + D3 = 0 + -3 Reorder the terms: 3 + -3 + -1D + -3D2 + D3 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1D + -3D2 + D3 = 0 + -3 -1D + -3D2 + D3 = 0 + -3 Combine like terms: 0 + -3 = -3 -1D + -3D2 + D3 = -3 Add 'D' to each side of the equation. -1D + -3D2 + D + D3 = -3 + D Reorder the terms: -1D + D + -3D2 + D3 = -3 + D Combine like terms: -1D + D = 0 0 + -3D2 + D3 = -3 + D -3D2 + D3 = -3 + D Add '3D2' to each side of the equation. -3D2 + 3D2 + D3 = -3 + D + 3D2 Combine like terms: -3D2 + 3D2 = 0 0 + D3 = -3 + D + 3D2 D3 = -3 + D + 3D2 Add '-1D3' to each side of the equation. D3 + -1D3 = -3 + D + 3D2 + -1D3 Combine like terms: D3 + -1D3 = 0 0 = -3 + D + 3D2 + -1D3 Simplifying 0 = -3 + D + 3D2 + -1D3 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

y = {0}

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