(-2xy^2)dx+(4y^3-2x^2y+1)dy=0

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Solution for (-2xy^2)dx+(4y^3-2x^2y+1)dy=0 equation: 


Simplifying
(-2xy2) * dx + (4y3 + -2x2y + 1) * dy = 0

Remove parenthesis around (-2xy2)
-2xy2 * dx + (4y3 + -2x2y + 1) * dy = 0

Multiply xy2 * dx
-2dx2y2 + (4y3 + -2x2y + 1) * dy = 0

Reorder the terms:
-2dx2y2 + (1 + -2x2y + 4y3) * dy = 0

Reorder the terms for easier multiplication:
-2dx2y2 + dy(1 + -2x2y + 4y3) = 0
-2dx2y2 + (1 * dy + -2x2y * dy + 4y3 * dy) = 0

Reorder the terms:
-2dx2y2 + (-2dx2y2 + 1dy + 4dy4) = 0
-2dx2y2 + (-2dx2y2 + 1dy + 4dy4) = 0

Combine like terms: -2dx2y2 + -2dx2y2 = -4dx2y2
-4dx2y2 + 1dy + 4dy4 = 0

Solving
-4dx2y2 + 1dy + 4dy4 = 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), 'dy'.
dy(-4x2y + 1 + 4y3) = 0


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

Simplifying
dy = 0

Solving
dy = 0

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

Simplifying
dy = 0

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 '(-4x2y + 1 + 4y3)' equal to zero and attempt to solve:

Simplifying
-4x2y + 1 + 4y3 = 0

Reorder the terms:
1 + -4x2y + 4y3 = 0

Solving
1 + -4x2y + 4y3 = 0

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

Add '-1' to each side of the equation.
1 + -4x2y + -1 + 4y3 = 0 + -1

Reorder the terms:
1 + -1 + -4x2y + 4y3 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x2y + 4y3 = 0 + -1
-4x2y + 4y3 = 0 + -1

Combine like terms: 0 + -1 = -1
-4x2y + 4y3 = -1

Add '4x2y' to each side of the equation.
-4x2y + 4x2y + 4y3 = -1 + 4x2y

Combine like terms: -4x2y + 4x2y = 0
0 + 4y3 = -1 + 4x2y
4y3 = -1 + 4x2y

Add '-4y3' to each side of the equation.
4y3 + -4y3 = -1 + 4x2y + -4y3

Combine like terms: 4y3 + -4y3 = 0
0 = -1 + 4x2y + -4y3

Simplifying
0 = -1 + 4x2y + -4y3

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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