(2XY^2-2Y)dx+(3X^2Y+4x)dy=0

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Solution for (2XY^2-2Y)dx+(3X^2Y+4x)dy=0 equation: 


Simplifying
(2XY2 + -2Y) * dx + (3X2Y + 4x) * dy = 0

Reorder the terms for easier multiplication:
dx(2XY2 + -2Y) + (3X2Y + 4x) * dy = 0
(2XY2 * dx + -2Y * dx) + (3X2Y + 4x) * dy = 0
(2dxXY2 + -2dxY) + (3X2Y + 4x) * dy = 0

Reorder the terms for easier multiplication:
2dxXY2 + -2dxY + dy(3X2Y + 4x) = 0
2dxXY2 + -2dxY + (3X2Y * dy + 4x * dy) = 0

Reorder the terms:
2dxXY2 + -2dxY + (4dxy + 3dyX2Y) = 0
2dxXY2 + -2dxY + (4dxy + 3dyX2Y) = 0

Solving
2dxXY2 + -2dxY + 4dxy + 3dyX2Y = 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(2xXY2 + -2xY + 4xy + 3yX2Y) = 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 '(2xXY2 + -2xY + 4xy + 3yX2Y)' equal to zero and attempt to solve:

Simplifying
2xXY2 + -2xY + 4xy + 3yX2Y = 0

Solving
2xXY2 + -2xY + 4xy + 3yX2Y = 0

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

Add '-2xXY2' to each side of the equation.
2xXY2 + -2xY + 4xy + -2xXY2 + 3yX2Y = 0 + -2xXY2

Reorder the terms:
2xXY2 + -2xXY2 + -2xY + 4xy + 3yX2Y = 0 + -2xXY2

Combine like terms: 2xXY2 + -2xXY2 = 0
0 + -2xY + 4xy + 3yX2Y = 0 + -2xXY2
-2xY + 4xy + 3yX2Y = 0 + -2xXY2
Remove the zero:
-2xY + 4xy + 3yX2Y = -2xXY2

Add '2xY' to each side of the equation.
-2xY + 4xy + 2xY + 3yX2Y = -2xXY2 + 2xY

Reorder the terms:
-2xY + 2xY + 4xy + 3yX2Y = -2xXY2 + 2xY

Combine like terms: -2xY + 2xY = 0
0 + 4xy + 3yX2Y = -2xXY2 + 2xY
4xy + 3yX2Y = -2xXY2 + 2xY

Add '-4xy' to each side of the equation.
4xy + -4xy + 3yX2Y = -2xXY2 + 2xY + -4xy

Combine like terms: 4xy + -4xy = 0
0 + 3yX2Y = -2xXY2 + 2xY + -4xy
3yX2Y = -2xXY2 + 2xY + -4xy

Add '-3yX2Y' to each side of the equation.
3yX2Y + -3yX2Y = -2xXY2 + 2xY + -4xy + -3yX2Y

Combine like terms: 3yX2Y + -3yX2Y = 0
0 = -2xXY2 + 2xY + -4xy + -3yX2Y

Simplifying
0 = -2xXY2 + 2xY + -4xy + -3yX2Y

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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