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

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


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

Multiply x * y
(x2 + xy + -1y2) * dx(-1x * y) * dy = 0

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

Multiply x * y
(xy + x2 + -1y2) * dx(-1xy) * dy = 0

Remove parenthesis around (-1xy)
(xy + x2 + -1y2) * dx * -1xy * dy = 0

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

Multiply dx * xy
-1dx2y * dy(xy + x2 + -1y2) = 0

Multiply dx2y * dy
-1d2x2y2(xy + x2 + -1y2) = 0
(xy * -1d2x2y2 + x2 * -1d2x2y2 + -1y2 * -1d2x2y2) = 0

Reorder the terms:
(1d2x2y4 + -1d2x3y3 + -1d2x4y2) = 0
(1d2x2y4 + -1d2x3y3 + -1d2x4y2) = 0

Solving
1d2x2y4 + -1d2x3y3 + -1d2x4y2 = 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), 'd2x2y2'.
d2x2y2(y2 + -1xy + -1x2) = 0

Subproblem 1

Set the factor 'd2x2y2' equal to zero and attempt to solve: Simplifying d2x2y2 = 0 Solving d2x2y2 = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d2x2y2 = 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 '(y2 + -1xy + -1x2)' equal to zero and attempt to solve: Simplifying y2 + -1xy + -1x2 = 0 Reorder the terms: -1xy + -1x2 + y2 = 0 Solving -1xy + -1x2 + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add 'xy' to each side of the equation. -1xy + -1x2 + xy + y2 = 0 + xy Reorder the terms: -1xy + xy + -1x2 + y2 = 0 + xy Combine like terms: -1xy + xy = 0 0 + -1x2 + y2 = 0 + xy -1x2 + y2 = 0 + xy Remove the zero: -1x2 + y2 = xy Add 'x2' to each side of the equation. -1x2 + x2 + y2 = xy + x2 Combine like terms: -1x2 + x2 = 0 0 + y2 = xy + x2 y2 = xy + x2 Add '-1y2' to each side of the equation. y2 + -1y2 = xy + x2 + -1y2 Combine like terms: y2 + -1y2 = 0 0 = xy + x2 + -1y2 Simplifying 0 = xy + x2 + -1y2 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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