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

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


Simplifying
(Xy2 + x) * dx + (y + -1x2y) * dy = 0

Reorder the terms:
(x + y2X) * dx + (y + -1x2y) * dy = 0

Reorder the terms for easier multiplication:
dx(x + y2X) + (y + -1x2y) * dy = 0
(x * dx + y2X * dx) + (y + -1x2y) * dy = 0

Reorder the terms:
(dxy2X + dx2) + (y + -1x2y) * dy = 0
(dxy2X + dx2) + (y + -1x2y) * dy = 0

Reorder the terms:
dxy2X + dx2 + (-1x2y + y) * dy = 0

Reorder the terms for easier multiplication:
dxy2X + dx2 + dy(-1x2y + y) = 0
dxy2X + dx2 + (-1x2y * dy + y * dy) = 0
dxy2X + dx2 + (-1dx2y2 + dy2) = 0

Solving
dxy2X + dx2 + -1dx2y2 + dy2 = 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(xy2X + x2 + -1x2y2 + y2) = 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 '(xy2X + x2 + -1x2y2 + y2)' equal to zero and attempt to solve:

Simplifying
xy2X + x2 + -1x2y2 + y2 = 0

Solving
xy2X + x2 + -1x2y2 + y2 = 0

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

Add '-1xy2X' to each side of the equation.
xy2X + x2 + -1x2y2 + -1xy2X + y2 = 0 + -1xy2X

Reorder the terms:
xy2X + -1xy2X + x2 + -1x2y2 + y2 = 0 + -1xy2X

Combine like terms: xy2X + -1xy2X = 0
0 + x2 + -1x2y2 + y2 = 0 + -1xy2X
x2 + -1x2y2 + y2 = 0 + -1xy2X
Remove the zero:
x2 + -1x2y2 + y2 = -1xy2X

Add '-1x2' to each side of the equation.
x2 + -1x2y2 + -1x2 + y2 = -1xy2X + -1x2

Reorder the terms:
x2 + -1x2 + -1x2y2 + y2 = -1xy2X + -1x2

Combine like terms: x2 + -1x2 = 0
0 + -1x2y2 + y2 = -1xy2X + -1x2
-1x2y2 + y2 = -1xy2X + -1x2

Add 'x2y2' to each side of the equation.
-1x2y2 + x2y2 + y2 = -1xy2X + -1x2 + x2y2

Combine like terms: -1x2y2 + x2y2 = 0
0 + y2 = -1xy2X + -1x2 + x2y2
y2 = -1xy2X + -1x2 + x2y2

Add '-1y2' to each side of the equation.
y2 + -1y2 = -1xy2X + -1x2 + x2y2 + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -1xy2X + -1x2 + x2y2 + -1y2

Simplifying
0 = -1xy2X + -1x2 + x2y2 + -1y2

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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