(D^4-2D^3+3D^2+1)y=0

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Solution for (D^4-2D^3+3D^2+1)y=0 equation: 


Simplifying
(D4 + -2D3 + 3D2 + 1) * y = 0

Reorder the terms:
(1 + 3D2 + -2D3 + D4) * y = 0

Reorder the terms for easier multiplication:
y(1 + 3D2 + -2D3 + D4) = 0
(1 * y + 3D2 * y + -2D3 * y + D4 * y) = 0
(1y + 3yD2 + -2yD3 + yD4) = 0

Solving
1y + 3yD2 + -2yD3 + yD4 = 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(1 + 3D2 + -2D3 + D4) = 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 '(1 + 3D2 + -2D3 + D4)' equal to zero and attempt to solve:

Simplifying
1 + 3D2 + -2D3 + D4 = 0

Solving
1 + 3D2 + -2D3 + D4 = 0

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

Add '-1' to each side of the equation.
1 + 3D2 + -2D3 + -1 + D4 = 0 + -1

Reorder the terms:
1 + -1 + 3D2 + -2D3 + D4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3D2 + -2D3 + D4 = 0 + -1
3D2 + -2D3 + D4 = 0 + -1

Combine like terms: 0 + -1 = -1
3D2 + -2D3 + D4 = -1

Add '-3D2' to each side of the equation.
3D2 + -2D3 + -3D2 + D4 = -1 + -3D2

Reorder the terms:
3D2 + -3D2 + -2D3 + D4 = -1 + -3D2

Combine like terms: 3D2 + -3D2 = 0
0 + -2D3 + D4 = -1 + -3D2
-2D3 + D4 = -1 + -3D2

Add '2D3' to each side of the equation.
-2D3 + 2D3 + D4 = -1 + -3D2 + 2D3

Combine like terms: -2D3 + 2D3 = 0
0 + D4 = -1 + -3D2 + 2D3
D4 = -1 + -3D2 + 2D3

Add '-1D4' to each side of the equation.
D4 + -1D4 = -1 + -3D2 + 2D3 + -1D4

Combine like terms: D4 + -1D4 = 0
0 = -1 + -3D2 + 2D3 + -1D4

Simplifying
0 = -1 + -3D2 + 2D3 + -1D4

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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