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

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


Simplifying
(y2 + xy2) * dy + (x2 + -1yx2) * dx = 0

Reorder the terms:
(xy2 + y2) * dy + (x2 + -1yx2) * dx = 0

Reorder the terms for easier multiplication:
dy(xy2 + y2) + (x2 + -1yx2) * dx = 0
(xy2 * dy + y2 * dy) + (x2 + -1yx2) * dx = 0
(dxy3 + dy3) + (x2 + -1yx2) * dx = 0

Reorder the terms for easier multiplication:
dxy3 + dy3 + dx(x2 + -1x2y) = 0
dxy3 + dy3 + (x2 * dx + -1x2y * dx) = 0
dxy3 + dy3 + (dx3 + -1dx3y) = 0

Reorder the terms:
dxy3 + dx3 + -1dx3y + dy3 = 0

Solving
dxy3 + dx3 + -1dx3y + dy3 = 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 + x3 + -1x3y + y3) = 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 + x3 + -1x3y + y3)' equal to zero and attempt to solve:

Simplifying
xy3 + x3 + -1x3y + y3 = 0

Solving
xy3 + x3 + -1x3y + y3 = 0

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

Add '-1xy3' to each side of the equation.
xy3 + x3 + -1x3y + -1xy3 + y3 = 0 + -1xy3

Reorder the terms:
xy3 + -1xy3 + x3 + -1x3y + y3 = 0 + -1xy3

Combine like terms: xy3 + -1xy3 = 0
0 + x3 + -1x3y + y3 = 0 + -1xy3
x3 + -1x3y + y3 = 0 + -1xy3
Remove the zero:
x3 + -1x3y + y3 = -1xy3

Add '-1x3' to each side of the equation.
x3 + -1x3y + -1x3 + y3 = -1xy3 + -1x3

Reorder the terms:
x3 + -1x3 + -1x3y + y3 = -1xy3 + -1x3

Combine like terms: x3 + -1x3 = 0
0 + -1x3y + y3 = -1xy3 + -1x3
-1x3y + y3 = -1xy3 + -1x3

Add 'x3y' to each side of the equation.
-1x3y + x3y + y3 = -1xy3 + -1x3 + x3y

Combine like terms: -1x3y + x3y = 0
0 + y3 = -1xy3 + -1x3 + x3y
y3 = -1xy3 + -1x3 + x3y

Add '-1y3' to each side of the equation.
y3 + -1y3 = -1xy3 + -1x3 + x3y + -1y3

Combine like terms: y3 + -1y3 = 0
0 = -1xy3 + -1x3 + x3y + -1y3

Simplifying
0 = -1xy3 + -1x3 + x3y + -1y3

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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