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

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


Simplifying
(xy2 + -4x) * dx + (3y2 + xy2) * dy = 0

Reorder the terms:
(-4x + xy2) * dx + (3y2 + xy2) * dy = 0

Reorder the terms for easier multiplication:
dx(-4x + xy2) + (3y2 + xy2) * dy = 0
(-4x * dx + xy2 * dx) + (3y2 + xy2) * dy = 0
(-4dx2 + dx2y2) + (3y2 + xy2) * dy = 0

Reorder the terms:
-4dx2 + dx2y2 + (xy2 + 3y2) * dy = 0

Reorder the terms for easier multiplication:
-4dx2 + dx2y2 + dy(xy2 + 3y2) = 0
-4dx2 + dx2y2 + (xy2 * dy + 3y2 * dy) = 0
-4dx2 + dx2y2 + (dxy3 + 3dy3) = 0

Reorder the terms:
dxy3 + -4dx2 + dx2y2 + 3dy3 = 0

Solving
dxy3 + -4dx2 + dx2y2 + 3dy3 = 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(xy3 + -4x2 + x2y2 + 3y3) = 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 '(xy3 + -4x2 + x2y2 + 3y3)' equal to zero and attempt to solve:

Simplifying
xy3 + -4x2 + x2y2 + 3y3 = 0

Solving
xy3 + -4x2 + x2y2 + 3y3 = 0

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

Add '-1xy3' to each side of the equation.
xy3 + -4x2 + x2y2 + -1xy3 + 3y3 = 0 + -1xy3

Reorder the terms:
xy3 + -1xy3 + -4x2 + x2y2 + 3y3 = 0 + -1xy3

Combine like terms: xy3 + -1xy3 = 0
0 + -4x2 + x2y2 + 3y3 = 0 + -1xy3
-4x2 + x2y2 + 3y3 = 0 + -1xy3
Remove the zero:
-4x2 + x2y2 + 3y3 = -1xy3

Add '4x2' to each side of the equation.
-4x2 + x2y2 + 4x2 + 3y3 = -1xy3 + 4x2

Reorder the terms:
-4x2 + 4x2 + x2y2 + 3y3 = -1xy3 + 4x2

Combine like terms: -4x2 + 4x2 = 0
0 + x2y2 + 3y3 = -1xy3 + 4x2
x2y2 + 3y3 = -1xy3 + 4x2

Add '-1x2y2' to each side of the equation.
x2y2 + -1x2y2 + 3y3 = -1xy3 + 4x2 + -1x2y2

Combine like terms: x2y2 + -1x2y2 = 0
0 + 3y3 = -1xy3 + 4x2 + -1x2y2
3y3 = -1xy3 + 4x2 + -1x2y2

Add '-3y3' to each side of the equation.
3y3 + -3y3 = -1xy3 + 4x2 + -1x2y2 + -3y3

Combine like terms: 3y3 + -3y3 = 0
0 = -1xy3 + 4x2 + -1x2y2 + -3y3

Simplifying
0 = -1xy3 + 4x2 + -1x2y2 + -3y3

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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