x^2(y+1)dx+y^2(x-1)dy=0

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Solution for x^2(y+1)dx+y^2(x-1)dy=0 equation: 


Simplifying
x2(y + 1) * dx + y2(x + -1) * dy = 0

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

Reorder the terms for easier multiplication:
x2 * dx(1 + y) + y2(x + -1) * dy = 0

Multiply x2 * dx
dx3(1 + y) + y2(x + -1) * dy = 0
(1 * dx3 + y * dx3) + y2(x + -1) * dy = 0
(1dx3 + dx3y) + y2(x + -1) * dy = 0

Reorder the terms:
1dx3 + dx3y + y2(-1 + x) * dy = 0

Reorder the terms for easier multiplication:
1dx3 + dx3y + y2 * dy(-1 + x) = 0

Multiply y2 * dy
1dx3 + dx3y + dy3(-1 + x) = 0
1dx3 + dx3y + (-1 * dy3 + x * dy3) = 0

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

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

Solving
dxy3 + 1dx3 + dx3y + -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(xy3 + x3 + x3y + -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 '(xy3 + x3 + x3y + -1y3)' equal to zero and attempt to solve:

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

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

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

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

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

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

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

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

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

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

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

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