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

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


Simplifying
(xy + x) * dx + -1(y + x2 * y) * dy = 0

Reorder the terms:
(x + xy) * dx + -1(y + x2 * y) * dy = 0

Reorder the terms for easier multiplication:
dx(x + xy) + -1(y + x2 * y) * dy = 0
(x * dx + xy * dx) + -1(y + x2 * y) * dy = 0
(dx2 + dx2y) + -1(y + x2 * y) * dy = 0

Multiply x2 * y
dx2 + dx2y + -1(y + x2y) * dy = 0

Reorder the terms:
dx2 + dx2y + -1(x2y + y) * dy = 0

Reorder the terms for easier multiplication:
dx2 + dx2y + -1dy(x2y + y) = 0
dx2 + dx2y + (x2y * -1dy + y * -1dy) = 0
dx2 + dx2y + (-1dx2y2 + -1dy2) = 0

Solving
dx2 + dx2y + -1dx2y2 + -1dy2 = 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 + x2y + -1x2y2 + -1y2) = 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 + x2y + -1x2y2 + -1y2)' equal to zero and attempt to solve:

Simplifying
x2 + x2y + -1x2y2 + -1y2 = 0

Solving
x2 + x2y + -1x2y2 + -1y2 = 0

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

Add '-1x2' to each side of the equation.
x2 + x2y + -1x2y2 + -1x2 + -1y2 = 0 + -1x2

Reorder the terms:
x2 + -1x2 + x2y + -1x2y2 + -1y2 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
0 + x2y + -1x2y2 + -1y2 = 0 + -1x2
x2y + -1x2y2 + -1y2 = 0 + -1x2
Remove the zero:
x2y + -1x2y2 + -1y2 = -1x2

Add '-1x2y' to each side of the equation.
x2y + -1x2y2 + -1x2y + -1y2 = -1x2 + -1x2y

Reorder the terms:
x2y + -1x2y + -1x2y2 + -1y2 = -1x2 + -1x2y

Combine like terms: x2y + -1x2y = 0
0 + -1x2y2 + -1y2 = -1x2 + -1x2y
-1x2y2 + -1y2 = -1x2 + -1x2y

Add 'x2y2' to each side of the equation.
-1x2y2 + x2y2 + -1y2 = -1x2 + -1x2y + x2y2

Combine like terms: -1x2y2 + x2y2 = 0
0 + -1y2 = -1x2 + -1x2y + x2y2
-1y2 = -1x2 + -1x2y + x2y2

Add 'y2' to each side of the equation.
-1y2 + y2 = -1x2 + -1x2y + x2y2 + y2

Combine like terms: -1y2 + y2 = 0
0 = -1x2 + -1x2y + x2y2 + y2

Simplifying
0 = -1x2 + -1x2y + x2y2 + y2

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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