(2yx-2)DX+(x^2-2x)Du=0

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Solution for (2yx-2)DX+(x^2-2x)Du=0 equation: 


Simplifying
(2yx + -2) * DX + (x2 + -2x) * Du = 0

Reorder the terms:
(-2 + 2xy) * DX + (x2 + -2x) * Du = 0

Reorder the terms for easier multiplication:
DX(-2 + 2xy) + (x2 + -2x) * Du = 0
(-2 * DX + 2xy * DX) + (x2 + -2x) * Du = 0
(-2DX + 2xyDX) + (x2 + -2x) * Du = 0

Reorder the terms:
-2DX + 2xyDX + (-2x + x2) * Du = 0

Reorder the terms for easier multiplication:
-2DX + 2xyDX + uD(-2x + x2) = 0
-2DX + 2xyDX + (-2x * uD + x2 * uD) = 0
-2DX + 2xyDX + (-2uxD + ux2D) = 0

Reorder the terms:
-2DX + -2uxD + ux2D + 2xyDX = 0

Solving
-2DX + -2uxD + ux2D + 2xyDX = 0

Solving for variable 'D'.

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

Factor out the Greatest Common Factor (GCF), 'D'.
D(-2X + -2ux + ux2 + 2xyX) = 0


Subproblem 1
Set the factor 'D' equal to zero and attempt to solve:

Simplifying
D = 0

Solving
D = 0

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

Simplifying
D = 0

Subproblem 2
Set the factor '(-2X + -2ux + ux2 + 2xyX)' equal to zero and attempt to solve:

Simplifying
-2X + -2ux + ux2 + 2xyX = 0

Solving
-2X + -2ux + ux2 + 2xyX = 0

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

Add '2X' to each side of the equation.
-2X + -2ux + ux2 + 2X + 2xyX = 0 + 2X

Reorder the terms:
-2X + 2X + -2ux + ux2 + 2xyX = 0 + 2X

Combine like terms: -2X + 2X = 0
0 + -2ux + ux2 + 2xyX = 0 + 2X
-2ux + ux2 + 2xyX = 0 + 2X
Remove the zero:
-2ux + ux2 + 2xyX = 2X

Add '2ux' to each side of the equation.
-2ux + ux2 + 2ux + 2xyX = 2X + 2ux

Reorder the terms:
-2ux + 2ux + ux2 + 2xyX = 2X + 2ux

Combine like terms: -2ux + 2ux = 0
0 + ux2 + 2xyX = 2X + 2ux
ux2 + 2xyX = 2X + 2ux

Add '-1ux2' to each side of the equation.
ux2 + -1ux2 + 2xyX = 2X + 2ux + -1ux2

Combine like terms: ux2 + -1ux2 = 0
0 + 2xyX = 2X + 2ux + -1ux2
2xyX = 2X + 2ux + -1ux2

Add '-2xyX' to each side of the equation.
2xyX + -2xyX = 2X + 2ux + -1ux2 + -2xyX

Combine like terms: 2xyX + -2xyX = 0
0 = 2X + 2ux + -1ux2 + -2xyX

Simplifying
0 = 2X + 2ux + -1ux2 + -2xyX

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
D = {0}

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