(2yx-2y)DX+(x^2-2x)dy=0

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


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

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

Reorder the terms:
2xyDX + -2yDX + (-2x + x2) * dy = 0

Reorder the terms for easier multiplication:
2xyDX + -2yDX + dy(-2x + x2) = 0
2xyDX + -2yDX + (-2x * dy + x2 * dy) = 0
2xyDX + -2yDX + (-2dxy + dx2y) = 0

Reorder the terms:
-2dxy + dx2y + 2xyDX + -2yDX = 0

Solving
-2dxy + dx2y + 2xyDX + -2yDX = 0

Solving for variable 'd'.

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

Add '-2xyDX' to each side of the equation.
-2dxy + dx2y + 2xyDX + -2xyDX + -2yDX = 0 + -2xyDX

Combine like terms: 2xyDX + -2xyDX = 0
-2dxy + dx2y + 0 + -2yDX = 0 + -2xyDX
-2dxy + dx2y + -2yDX = 0 + -2xyDX
Remove the zero:
-2dxy + dx2y + -2yDX = -2xyDX

Add '2yDX' to each side of the equation.
-2dxy + dx2y + -2yDX + 2yDX = -2xyDX + 2yDX

Combine like terms: -2yDX + 2yDX = 0
-2dxy + dx2y + 0 = -2xyDX + 2yDX
-2dxy + dx2y = -2xyDX + 2yDX

Reorder the terms:
-2dxy + dx2y + 2xyDX + -2yDX = -2xyDX + 2xyDX + 2yDX + -2yDX

Combine like terms: -2xyDX + 2xyDX = 0
-2dxy + dx2y + 2xyDX + -2yDX = 0 + 2yDX + -2yDX
-2dxy + dx2y + 2xyDX + -2yDX = 2yDX + -2yDX

Combine like terms: 2yDX + -2yDX = 0
-2dxy + dx2y + 2xyDX + -2yDX = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(-2dx + dx2 + 2xDX + -2DX) = 0


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

Simplifying
y = 0

Solving
y = 0

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

Add '-1y' to each side of the equation.
y + -1y = 0 + -1y
Remove the zero:
0 = -1y

Simplifying
0 = -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-2dx + dx2 + 2xDX + -2DX)' equal to zero and attempt to solve:

Simplifying
-2dx + dx2 + 2xDX + -2DX = 0

Reorder the terms:
-2DX + -2dx + dx2 + 2xDX = 0

Solving
-2DX + -2dx + dx2 + 2xDX = 0

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

Add '2DX' to each side of the equation.
-2DX + -2dx + dx2 + 2DX + 2xDX = 0 + 2DX

Reorder the terms:
-2DX + 2DX + -2dx + dx2 + 2xDX = 0 + 2DX

Combine like terms: -2DX + 2DX = 0
0 + -2dx + dx2 + 2xDX = 0 + 2DX
-2dx + dx2 + 2xDX = 0 + 2DX
Remove the zero:
-2dx + dx2 + 2xDX = 2DX

Add '-2xDX' to each side of the equation.
-2dx + dx2 + 2xDX + -2xDX = 2DX + -2xDX

Combine like terms: 2xDX + -2xDX = 0
-2dx + dx2 + 0 = 2DX + -2xDX
-2dx + dx2 = 2DX + -2xDX

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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