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

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


Simplifying
2x + -2y + -1 + y(x + y + -2) * dy = 0

Reorder the terms:
2x + -2y + -1 + y(-2 + x + y) * dy = 0

Reorder the terms for easier multiplication:
2x + -2y + -1 + y * dy(-2 + x + y) = 0

Multiply y * dy
2x + -2y + -1 + dy2(-2 + x + y) = 0
2x + -2y + -1 + (-2 * dy2 + x * dy2 + y * dy2) = 0

Reorder the terms:
2x + -2y + -1 + (dxy2 + -2dy2 + dy3) = 0
2x + -2y + -1 + (dxy2 + -2dy2 + dy3) = 0

Reorder the terms:
-1 + dxy2 + -2dy2 + dy3 + 2x + -2y = 0

Solving
-1 + dxy2 + -2dy2 + dy3 + 2x + -2y = 0

Solving for variable 'd'.

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

Add '1' to each side of the equation.
-1 + dxy2 + -2dy2 + dy3 + 2x + 1 + -2y = 0 + 1

Reorder the terms:
-1 + 1 + dxy2 + -2dy2 + dy3 + 2x + -2y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + dxy2 + -2dy2 + dy3 + 2x + -2y = 0 + 1
dxy2 + -2dy2 + dy3 + 2x + -2y = 0 + 1

Combine like terms: 0 + 1 = 1
dxy2 + -2dy2 + dy3 + 2x + -2y = 1

Add '-2x' to each side of the equation.
dxy2 + -2dy2 + dy3 + 2x + -2x + -2y = 1 + -2x

Combine like terms: 2x + -2x = 0
dxy2 + -2dy2 + dy3 + 0 + -2y = 1 + -2x
dxy2 + -2dy2 + dy3 + -2y = 1 + -2x

Add '2y' to each side of the equation.
dxy2 + -2dy2 + dy3 + -2y + 2y = 1 + -2x + 2y

Combine like terms: -2y + 2y = 0
dxy2 + -2dy2 + dy3 + 0 = 1 + -2x + 2y
dxy2 + -2dy2 + dy3 = 1 + -2x + 2y

Reorder the terms:
-1 + dxy2 + -2dy2 + dy3 + 2x + -2y = 1 + -2x + 2y + -1 + 2x + -2y

Reorder the terms:
-1 + dxy2 + -2dy2 + dy3 + 2x + -2y = 1 + -1 + -2x + 2x + 2y + -2y

Combine like terms: 1 + -1 = 0
-1 + dxy2 + -2dy2 + dy3 + 2x + -2y = 0 + -2x + 2x + 2y + -2y
-1 + dxy2 + -2dy2 + dy3 + 2x + -2y = -2x + 2x + 2y + -2y

Combine like terms: -2x + 2x = 0
-1 + dxy2 + -2dy2 + dy3 + 2x + -2y = 0 + 2y + -2y
-1 + dxy2 + -2dy2 + dy3 + 2x + -2y = 2y + -2y

Combine like terms: 2y + -2y = 0
-1 + dxy2 + -2dy2 + dy3 + 2x + -2y = 0

The solution to this equation could not be determined.

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