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

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


Simplifying
(2x + -1y2 + 1) * dx + (2x + -1y2 + 1) * dy = 0

Reorder the terms:
(1 + 2x + -1y2) * dx + (2x + -1y2 + 1) * dy = 0

Reorder the terms for easier multiplication:
dx(1 + 2x + -1y2) + (2x + -1y2 + 1) * dy = 0
(1 * dx + 2x * dx + -1y2 * dx) + (2x + -1y2 + 1) * dy = 0

Reorder the terms:
(1dx + -1dxy2 + 2dx2) + (2x + -1y2 + 1) * dy = 0
(1dx + -1dxy2 + 2dx2) + (2x + -1y2 + 1) * dy = 0

Reorder the terms:
1dx + -1dxy2 + 2dx2 + (1 + 2x + -1y2) * dy = 0

Reorder the terms for easier multiplication:
1dx + -1dxy2 + 2dx2 + dy(1 + 2x + -1y2) = 0
1dx + -1dxy2 + 2dx2 + (1 * dy + 2x * dy + -1y2 * dy) = 0

Reorder the terms:
1dx + -1dxy2 + 2dx2 + (2dxy + 1dy + -1dy3) = 0
1dx + -1dxy2 + 2dx2 + (2dxy + 1dy + -1dy3) = 0

Reorder the terms:
1dx + 2dxy + -1dxy2 + 2dx2 + 1dy + -1dy3 = 0

Solving
1dx + 2dxy + -1dxy2 + 2dx2 + 1dy + -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(x + 2xy + -1xy2 + 2x2 + y + -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 '(x + 2xy + -1xy2 + 2x2 + y + -1y3)' equal to zero and attempt to solve: Simplifying x + 2xy + -1xy2 + 2x2 + y + -1y3 = 0 Solving x + 2xy + -1xy2 + 2x2 + y + -1y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + 2xy + -1xy2 + 2x2 + y + -1x + -1y3 = 0 + -1x Reorder the terms: x + -1x + 2xy + -1xy2 + 2x2 + y + -1y3 = 0 + -1x Combine like terms: x + -1x = 0 0 + 2xy + -1xy2 + 2x2 + y + -1y3 = 0 + -1x 2xy + -1xy2 + 2x2 + y + -1y3 = 0 + -1x Remove the zero: 2xy + -1xy2 + 2x2 + y + -1y3 = -1x Add '-2xy' to each side of the equation. 2xy + -1xy2 + 2x2 + y + -2xy + -1y3 = -1x + -2xy Reorder the terms: 2xy + -2xy + -1xy2 + 2x2 + y + -1y3 = -1x + -2xy Combine like terms: 2xy + -2xy = 0 0 + -1xy2 + 2x2 + y + -1y3 = -1x + -2xy -1xy2 + 2x2 + y + -1y3 = -1x + -2xy Add 'xy2' to each side of the equation. -1xy2 + 2x2 + y + xy2 + -1y3 = -1x + -2xy + xy2 Reorder the terms: -1xy2 + xy2 + 2x2 + y + -1y3 = -1x + -2xy + xy2 Combine like terms: -1xy2 + xy2 = 0 0 + 2x2 + y + -1y3 = -1x + -2xy + xy2 2x2 + y + -1y3 = -1x + -2xy + xy2 Add '-2x2' to each side of the equation. 2x2 + y + -2x2 + -1y3 = -1x + -2xy + xy2 + -2x2 Reorder the terms: 2x2 + -2x2 + y + -1y3 = -1x + -2xy + xy2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + y + -1y3 = -1x + -2xy + xy2 + -2x2 y + -1y3 = -1x + -2xy + xy2 + -2x2 Add '-1y' to each side of the equation. y + -1y + -1y3 = -1x + -2xy + xy2 + -2x2 + -1y Combine like terms: y + -1y = 0 0 + -1y3 = -1x + -2xy + xy2 + -2x2 + -1y -1y3 = -1x + -2xy + xy2 + -2x2 + -1y Add 'y3' to each side of the equation. -1y3 + y3 = -1x + -2xy + xy2 + -2x2 + -1y + y3 Combine like terms: -1y3 + y3 = 0 0 = -1x + -2xy + xy2 + -2x2 + -1y + y3 Simplifying 0 = -1x + -2xy + xy2 + -2x2 + -1y + 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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