Y(1-x)DX+x(1+y)dy=0

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Solution for Y(1-x)DX+x(1+y)dy=0 equation: 


Simplifying
Y(1 + -1x) * DX + x(1 + y) * dy = 0

Reorder the terms for easier multiplication:
Y * DX(1 + -1x) + x(1 + y) * dy = 0

Multiply Y * DX
DXY(1 + -1x) + x(1 + y) * dy = 0
(1 * DXY + -1x * DXY) + x(1 + y) * dy = 0
(1DXY + -1xDXY) + x(1 + y) * dy = 0

Reorder the terms for easier multiplication:
1DXY + -1xDXY + x * dy(1 + y) = 0

Multiply x * dy
1DXY + -1xDXY + dxy(1 + y) = 0
1DXY + -1xDXY + (1 * dxy + y * dxy) = 0
1DXY + -1xDXY + (1dxy + dxy2) = 0

Reorder the terms:
1DXY + 1dxy + dxy2 + -1xDXY = 0

Solving
1DXY + 1dxy + dxy2 + -1xDXY = 0

Solving for variable 'D'.

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

Add '-1dxy' to each side of the equation.
1DXY + 1dxy + dxy2 + -1dxy + -1xDXY = 0 + -1dxy

Reorder the terms:
1DXY + 1dxy + -1dxy + dxy2 + -1xDXY = 0 + -1dxy

Combine like terms: 1dxy + -1dxy = 0
1DXY + 0 + dxy2 + -1xDXY = 0 + -1dxy
1DXY + dxy2 + -1xDXY = 0 + -1dxy
Remove the zero:
1DXY + dxy2 + -1xDXY = -1dxy

Add '-1dxy2' to each side of the equation.
1DXY + dxy2 + -1dxy2 + -1xDXY = -1dxy + -1dxy2

Combine like terms: dxy2 + -1dxy2 = 0
1DXY + 0 + -1xDXY = -1dxy + -1dxy2
1DXY + -1xDXY = -1dxy + -1dxy2

Reorder the terms:
1DXY + dxy + dxy2 + -1xDXY = -1dxy + -1dxy2 + dxy + dxy2

Reorder the terms:
1DXY + dxy + dxy2 + -1xDXY = -1dxy + dxy + -1dxy2 + dxy2

Combine like terms: -1dxy + dxy = 0
1DXY + dxy + dxy2 + -1xDXY = 0 + -1dxy2 + dxy2
1DXY + dxy + dxy2 + -1xDXY = -1dxy2 + dxy2

Combine like terms: -1dxy2 + dxy2 = 0
1DXY + dxy + dxy2 + -1xDXY = 0

The solution to this equation could not be determined.

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