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

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


Simplifying
(Xy + x) * dx + -1(x2y2 + x2 + y2 + 1) * dy = 0

Reorder the terms:
(x + yX) * dx + -1(x2y2 + x2 + y2 + 1) * dy = 0

Reorder the terms for easier multiplication:
dx(x + yX) + -1(x2y2 + x2 + y2 + 1) * dy = 0
(x * dx + yX * dx) + -1(x2y2 + x2 + y2 + 1) * dy = 0

Reorder the terms:
(dxyX + dx2) + -1(x2y2 + x2 + y2 + 1) * dy = 0
(dxyX + dx2) + -1(x2y2 + x2 + y2 + 1) * dy = 0

Reorder the terms:
dxyX + dx2 + -1(1 + x2 + x2y2 + y2) * dy = 0

Reorder the terms for easier multiplication:
dxyX + dx2 + -1dy(1 + x2 + x2y2 + y2) = 0
dxyX + dx2 + (1 * -1dy + x2 * -1dy + x2y2 * -1dy + y2 * -1dy) = 0

Reorder the terms:
dxyX + dx2 + (-1dx2y + -1dx2y3 + -1dy + -1dy3) = 0
dxyX + dx2 + (-1dx2y + -1dx2y3 + -1dy + -1dy3) = 0

Solving
dxyX + dx2 + -1dx2y + -1dx2y3 + -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(xyX + x2 + -1x2y + -1x2y3 + -1y + -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 '(xyX + x2 + -1x2y + -1x2y3 + -1y + -1y3)' equal to zero and attempt to solve: Simplifying xyX + x2 + -1x2y + -1x2y3 + -1y + -1y3 = 0 Solving xyX + x2 + -1x2y + -1x2y3 + -1y + -1y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1xyX' to each side of the equation. xyX + x2 + -1x2y + -1x2y3 + -1y + -1xyX + -1y3 = 0 + -1xyX Reorder the terms: xyX + -1xyX + x2 + -1x2y + -1x2y3 + -1y + -1y3 = 0 + -1xyX Combine like terms: xyX + -1xyX = 0 0 + x2 + -1x2y + -1x2y3 + -1y + -1y3 = 0 + -1xyX x2 + -1x2y + -1x2y3 + -1y + -1y3 = 0 + -1xyX Remove the zero: x2 + -1x2y + -1x2y3 + -1y + -1y3 = -1xyX Add '-1x2' to each side of the equation. x2 + -1x2y + -1x2y3 + -1y + -1x2 + -1y3 = -1xyX + -1x2 Reorder the terms: x2 + -1x2 + -1x2y + -1x2y3 + -1y + -1y3 = -1xyX + -1x2 Combine like terms: x2 + -1x2 = 0 0 + -1x2y + -1x2y3 + -1y + -1y3 = -1xyX + -1x2 -1x2y + -1x2y3 + -1y + -1y3 = -1xyX + -1x2 Add 'x2y' to each side of the equation. -1x2y + -1x2y3 + -1y + x2y + -1y3 = -1xyX + -1x2 + x2y Reorder the terms: -1x2y + x2y + -1x2y3 + -1y + -1y3 = -1xyX + -1x2 + x2y Combine like terms: -1x2y + x2y = 0 0 + -1x2y3 + -1y + -1y3 = -1xyX + -1x2 + x2y -1x2y3 + -1y + -1y3 = -1xyX + -1x2 + x2y Add 'x2y3' to each side of the equation. -1x2y3 + -1y + x2y3 + -1y3 = -1xyX + -1x2 + x2y + x2y3 Reorder the terms: -1x2y3 + x2y3 + -1y + -1y3 = -1xyX + -1x2 + x2y + x2y3 Combine like terms: -1x2y3 + x2y3 = 0 0 + -1y + -1y3 = -1xyX + -1x2 + x2y + x2y3 -1y + -1y3 = -1xyX + -1x2 + x2y + x2y3 Add 'y' to each side of the equation. -1y + y + -1y3 = -1xyX + -1x2 + x2y + x2y3 + y Combine like terms: -1y + y = 0 0 + -1y3 = -1xyX + -1x2 + x2y + x2y3 + y -1y3 = -1xyX + -1x2 + x2y + x2y3 + y Add 'y3' to each side of the equation. -1y3 + y3 = -1xyX + -1x2 + x2y + x2y3 + y + y3 Combine like terms: -1y3 + y3 = 0 0 = -1xyX + -1x2 + x2y + x2y3 + y + y3 Simplifying 0 = -1xyX + -1x2 + x2y + x2y3 + y + 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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