(1-2xy^2)dx+(2y-2x^2y)dy=0

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Solution for (1-2xy^2)dx+(2y-2x^2y)dy=0 equation: 


Simplifying
(1 + -2xy2) * dx + (2y + -2x2y) * dy = 0

Reorder the terms for easier multiplication:
dx(1 + -2xy2) + (2y + -2x2y) * dy = 0
(1 * dx + -2xy2 * dx) + (2y + -2x2y) * dy = 0
(1dx + -2dx2y2) + (2y + -2x2y) * dy = 0

Reorder the terms:
1dx + -2dx2y2 + (-2x2y + 2y) * dy = 0

Reorder the terms for easier multiplication:
1dx + -2dx2y2 + dy(-2x2y + 2y) = 0
1dx + -2dx2y2 + (-2x2y * dy + 2y * dy) = 0
1dx + -2dx2y2 + (-2dx2y2 + 2dy2) = 0

Combine like terms: -2dx2y2 + -2dx2y2 = -4dx2y2
1dx + -4dx2y2 + 2dy2 = 0

Solving
1dx + -4dx2y2 + 2dy2 = 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(x + -4x2y2 + 2y2) = 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 '(x + -4x2y2 + 2y2)' equal to zero and attempt to solve:

Simplifying
x + -4x2y2 + 2y2 = 0

Solving
x + -4x2y2 + 2y2 = 0

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

Add '-1x' to each side of the equation.
x + -4x2y2 + -1x + 2y2 = 0 + -1x

Reorder the terms:
x + -1x + -4x2y2 + 2y2 = 0 + -1x

Combine like terms: x + -1x = 0
0 + -4x2y2 + 2y2 = 0 + -1x
-4x2y2 + 2y2 = 0 + -1x
Remove the zero:
-4x2y2 + 2y2 = -1x

Add '4x2y2' to each side of the equation.
-4x2y2 + 4x2y2 + 2y2 = -1x + 4x2y2

Combine like terms: -4x2y2 + 4x2y2 = 0
0 + 2y2 = -1x + 4x2y2
2y2 = -1x + 4x2y2

Add '-2y2' to each side of the equation.
2y2 + -2y2 = -1x + 4x2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
0 = -1x + 4x2y2 + -2y2

Simplifying
0 = -1x + 4x2y2 + -2y2

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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