(x^2+y^2+x)dx+xy*dy=0

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Solution for (x^2+y^2+x)dx+xy*dy=0 equation:


Simplifying
(x2 + y2 + x) * dx + xy * dy = 0

Reorder the terms:
(x + x2 + y2) * dx + xy * dy = 0

Reorder the terms for easier multiplication:
dx(x + x2 + y2) + xy * dy = 0
(x * dx + x2 * dx + y2 * dx) + xy * dy = 0

Reorder the terms:
(dxy2 + dx2 + dx3) + xy * dy = 0
(dxy2 + dx2 + dx3) + xy * dy = 0

Multiply xy * dy
dxy2 + dx2 + dx3 + dxy2 = 0

Reorder the terms:
dxy2 + dxy2 + dx2 + dx3 = 0

Combine like terms: dxy2 + dxy2 = 2dxy2
2dxy2 + dx2 + dx3 = 0

Solving
2dxy2 + dx2 + dx3 = 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), 'dx'.
dx(2y2 + x + x2) = 0

Subproblem 1

Set the factor 'dx' equal to zero and attempt to solve: Simplifying dx = 0 Solving dx = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(2y2 + x + x2)' equal to zero and attempt to solve: Simplifying 2y2 + x + x2 = 0 Reorder the terms: x + x2 + 2y2 = 0 Solving x + x2 + 2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + x2 + -1x + 2y2 = 0 + -1x Reorder the terms: x + -1x + x2 + 2y2 = 0 + -1x Combine like terms: x + -1x = 0 0 + x2 + 2y2 = 0 + -1x x2 + 2y2 = 0 + -1x Remove the zero: x2 + 2y2 = -1x Add '-1x2' to each side of the equation. x2 + -1x2 + 2y2 = -1x + -1x2 Combine like terms: x2 + -1x2 = 0 0 + 2y2 = -1x + -1x2 2y2 = -1x + -1x2 Add '-2y2' to each side of the equation. 2y2 + -2y2 = -1x + -1x2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 0 = -1x + -1x2 + -2y2 Simplifying 0 = -1x + -1x2 + -2y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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