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

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


Simplifying
(xy3 + x) * dx + (x2y2 + -1y2) * dy = 0

Reorder the terms:
(x + xy3) * dx + (x2y2 + -1y2) * dy = 0

Reorder the terms for easier multiplication:
dx(x + xy3) + (x2y2 + -1y2) * dy = 0
(x * dx + xy3 * dx) + (x2y2 + -1y2) * dy = 0
(dx2 + dx2y3) + (x2y2 + -1y2) * dy = 0

Reorder the terms for easier multiplication:
dx2 + dx2y3 + dy(x2y2 + -1y2) = 0
dx2 + dx2y3 + (x2y2 * dy + -1y2 * dy) = 0
dx2 + dx2y3 + (dx2y3 + -1dy3) = 0

Combine like terms: dx2y3 + dx2y3 = 2dx2y3
dx2 + 2dx2y3 + -1dy3 = 0

Solving
dx2 + 2dx2y3 + -1dy3 = 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(x2 + 2x2y3 + -1y3) = 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 '(x2 + 2x2y3 + -1y3)' equal to zero and attempt to solve:

Simplifying
x2 + 2x2y3 + -1y3 = 0

Solving
x2 + 2x2y3 + -1y3 = 0

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

Add '-1x2' to each side of the equation.
x2 + 2x2y3 + -1x2 + -1y3 = 0 + -1x2

Reorder the terms:
x2 + -1x2 + 2x2y3 + -1y3 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
0 + 2x2y3 + -1y3 = 0 + -1x2
2x2y3 + -1y3 = 0 + -1x2
Remove the zero:
2x2y3 + -1y3 = -1x2

Add '-2x2y3' to each side of the equation.
2x2y3 + -2x2y3 + -1y3 = -1x2 + -2x2y3

Combine like terms: 2x2y3 + -2x2y3 = 0
0 + -1y3 = -1x2 + -2x2y3
-1y3 = -1x2 + -2x2y3

Add 'y3' to each side of the equation.
-1y3 + y3 = -1x2 + -2x2y3 + y3

Combine like terms: -1y3 + y3 = 0
0 = -1x2 + -2x2y3 + y3

Simplifying
0 = -1x2 + -2x2y3 + y3

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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