xdy+ydx=(x^3+3x^2y+3xy^2+y^3)+(dx+dy)

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Solution for xdy+ydx=(x^3+3x^2y+3xy^2+y^3)+(dx+dy) equation: 


Simplifying
xdy + ydx = (x3 + 3x2y + 3xy2 + y3) + (dx + dy)

Combine like terms: dxy + dxy = 2dxy
2dxy = (x3 + 3x2y + 3xy2 + y3) + (dx + dy)

Reorder the terms:
2dxy = (3xy2 + 3x2y + x3 + y3) + (dx + dy)

Remove parenthesis around (3xy2 + 3x2y + x3 + y3)
2dxy = 3xy2 + 3x2y + x3 + y3 + (dx + dy)

Remove parenthesis around (dx + dy)
2dxy = 3xy2 + 3x2y + x3 + y3 + dx + dy

Reorder the terms:
2dxy = dx + dy + 3xy2 + 3x2y + x3 + y3

Solving
2dxy = dx + dy + 3xy2 + 3x2y + x3 + y3

Solving for variable 'd'.

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

Add '-1dx' to each side of the equation.
-1dx + 2dxy = dx + dy + 3xy2 + 3x2y + x3 + -1dx + y3

Reorder the terms:
-1dx + 2dxy = dx + -1dx + dy + 3xy2 + 3x2y + x3 + y3

Combine like terms: dx + -1dx = 0
-1dx + 2dxy = 0 + dy + 3xy2 + 3x2y + x3 + y3
-1dx + 2dxy = dy + 3xy2 + 3x2y + x3 + y3

Add '-1dy' to each side of the equation.
-1dx + 2dxy + -1dy = dy + 3xy2 + 3x2y + x3 + -1dy + y3

Reorder the terms:
-1dx + 2dxy + -1dy = dy + -1dy + 3xy2 + 3x2y + x3 + y3

Combine like terms: dy + -1dy = 0
-1dx + 2dxy + -1dy = 0 + 3xy2 + 3x2y + x3 + y3
-1dx + 2dxy + -1dy = 3xy2 + 3x2y + x3 + y3

Reorder the terms:
-1dx + 2dxy + -1dy + -3xy2 + -3x2y + -1x3 + -1y3 = 3xy2 + -3xy2 + 3x2y + -3x2y + x3 + -1x3 + y3 + -1y3

Combine like terms: 3xy2 + -3xy2 = 0
-1dx + 2dxy + -1dy + -3xy2 + -3x2y + -1x3 + -1y3 = 0 + 3x2y + -3x2y + x3 + -1x3 + y3 + -1y3
-1dx + 2dxy + -1dy + -3xy2 + -3x2y + -1x3 + -1y3 = 3x2y + -3x2y + x3 + -1x3 + y3 + -1y3

Combine like terms: 3x2y + -3x2y = 0
-1dx + 2dxy + -1dy + -3xy2 + -3x2y + -1x3 + -1y3 = 0 + x3 + -1x3 + y3 + -1y3
-1dx + 2dxy + -1dy + -3xy2 + -3x2y + -1x3 + -1y3 = x3 + -1x3 + y3 + -1y3

Combine like terms: x3 + -1x3 = 0
-1dx + 2dxy + -1dy + -3xy2 + -3x2y + -1x3 + -1y3 = 0 + y3 + -1y3
-1dx + 2dxy + -1dy + -3xy2 + -3x2y + -1x3 + -1y3 = y3 + -1y3

Combine like terms: y3 + -1y3 = 0
-1dx + 2dxy + -1dy + -3xy2 + -3x2y + -1x3 + -1y3 = 0

The solution to this equation could not be determined.

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