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

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


Simplifying
(1 + 4xy + -4x2y) * dx + (x2 + -1x3) * dy = 0

Reorder the terms for easier multiplication:
dx(1 + 4xy + -4x2y) + (x2 + -1x3) * dy = 0
(1 * dx + 4xy * dx + -4x2y * dx) + (x2 + -1x3) * dy = 0
(1dx + 4dx2y + -4dx3y) + (x2 + -1x3) * dy = 0

Reorder the terms for easier multiplication:
1dx + 4dx2y + -4dx3y + dy(x2 + -1x3) = 0
1dx + 4dx2y + -4dx3y + (x2 * dy + -1x3 * dy) = 0
1dx + 4dx2y + -4dx3y + (dx2y + -1dx3y) = 0

Reorder the terms:
1dx + 4dx2y + dx2y + -4dx3y + -1dx3y = 0

Combine like terms: 4dx2y + dx2y = 5dx2y
1dx + 5dx2y + -4dx3y + -1dx3y = 0

Combine like terms: -4dx3y + -1dx3y = -5dx3y
1dx + 5dx2y + -5dx3y = 0

Solving
1dx + 5dx2y + -5dx3y = 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), 'dx'.
dx(1 + 5xy + -5x2y) = 0


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

Simplifying
dx = 0

Solving
dx = 0

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

Simplifying
dx = 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 '(1 + 5xy + -5x2y)' equal to zero and attempt to solve:

Simplifying
1 + 5xy + -5x2y = 0

Solving
1 + 5xy + -5x2y = 0

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

Add '-1' to each side of the equation.
1 + 5xy + -1 + -5x2y = 0 + -1

Reorder the terms:
1 + -1 + 5xy + -5x2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5xy + -5x2y = 0 + -1
5xy + -5x2y = 0 + -1

Combine like terms: 0 + -1 = -1
5xy + -5x2y = -1

Add '-5xy' to each side of the equation.
5xy + -5xy + -5x2y = -1 + -5xy

Combine like terms: 5xy + -5xy = 0
0 + -5x2y = -1 + -5xy
-5x2y = -1 + -5xy

Add '5x2y' to each side of the equation.
-5x2y + 5x2y = -1 + -5xy + 5x2y

Combine like terms: -5x2y + 5x2y = 0
0 = -1 + -5xy + 5x2y

Simplifying
0 = -1 + -5xy + 5x2y

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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