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

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


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

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

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

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

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

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

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

Solving
1dx3 + dx3y = -1dxy3 + 1dy3

Solving for variable 'd'.

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

Add 'dxy3' to each side of the equation.
1dx3 + dxy3 + dx3y = -1dxy3 + dxy3 + 1dy3

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

Combine like terms: -1dxy3 + dxy3 = 0
dxy3 + 1dx3 + dx3y = 0 + 1dy3
dxy3 + 1dx3 + dx3y = 1dy3

Add '-1dy3' to each side of the equation.
dxy3 + 1dx3 + dx3y + -1dy3 = 1dy3 + -1dy3

Combine like terms: 1dy3 + -1dy3 = 0
dxy3 + 1dx3 + dx3y + -1dy3 = 0

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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