(x^2-4*x*y-2*y^2)dx+(y^2-4*x*y-2*x^2)dy=0

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Solution for (x^2-4*x*y-2*y^2)dx+(y^2-4*x*y-2*x^2)dy=0 equation:


Simplifying
(x2 + -4x * y + -2y2) * dx + (y2 + -4x * y + -2x2) * dy = 0

Multiply x * y
(x2 + -4xy + -2y2) * dx + (y2 + -4x * y + -2x2) * dy = 0

Reorder the terms:
(-4xy + x2 + -2y2) * dx + (y2 + -4x * y + -2x2) * dy = 0

Reorder the terms for easier multiplication:
dx(-4xy + x2 + -2y2) + (y2 + -4x * y + -2x2) * dy = 0
(-4xy * dx + x2 * dx + -2y2 * dx) + (y2 + -4x * y + -2x2) * dy = 0

Reorder the terms:
(-2dxy2 + -4dx2y + dx3) + (y2 + -4x * y + -2x2) * dy = 0
(-2dxy2 + -4dx2y + dx3) + (y2 + -4x * y + -2x2) * dy = 0

Multiply x * y
-2dxy2 + -4dx2y + dx3 + (y2 + -4xy + -2x2) * dy = 0

Reorder the terms:
-2dxy2 + -4dx2y + dx3 + (-4xy + -2x2 + y2) * dy = 0

Reorder the terms for easier multiplication:
-2dxy2 + -4dx2y + dx3 + dy(-4xy + -2x2 + y2) = 0
-2dxy2 + -4dx2y + dx3 + (-4xy * dy + -2x2 * dy + y2 * dy) = 0
-2dxy2 + -4dx2y + dx3 + (-4dxy2 + -2dx2y + dy3) = 0

Reorder the terms:
-2dxy2 + -4dxy2 + -4dx2y + -2dx2y + dx3 + dy3 = 0

Combine like terms: -2dxy2 + -4dxy2 = -6dxy2
-6dxy2 + -4dx2y + -2dx2y + dx3 + dy3 = 0

Combine like terms: -4dx2y + -2dx2y = -6dx2y
-6dxy2 + -6dx2y + dx3 + dy3 = 0

Solving
-6dxy2 + -6dx2y + dx3 + dy3 = 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(-6xy2 + -6x2y + x3 + y3) = 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 '(-6xy2 + -6x2y + x3 + y3)' equal to zero and attempt to solve: Simplifying -6xy2 + -6x2y + x3 + y3 = 0 Solving -6xy2 + -6x2y + x3 + y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '6xy2' to each side of the equation. -6xy2 + -6x2y + x3 + 6xy2 + y3 = 0 + 6xy2 Reorder the terms: -6xy2 + 6xy2 + -6x2y + x3 + y3 = 0 + 6xy2 Combine like terms: -6xy2 + 6xy2 = 0 0 + -6x2y + x3 + y3 = 0 + 6xy2 -6x2y + x3 + y3 = 0 + 6xy2 Remove the zero: -6x2y + x3 + y3 = 6xy2 Add '6x2y' to each side of the equation. -6x2y + x3 + 6x2y + y3 = 6xy2 + 6x2y Reorder the terms: -6x2y + 6x2y + x3 + y3 = 6xy2 + 6x2y Combine like terms: -6x2y + 6x2y = 0 0 + x3 + y3 = 6xy2 + 6x2y x3 + y3 = 6xy2 + 6x2y Add '-1x3' to each side of the equation. x3 + -1x3 + y3 = 6xy2 + 6x2y + -1x3 Combine like terms: x3 + -1x3 = 0 0 + y3 = 6xy2 + 6x2y + -1x3 y3 = 6xy2 + 6x2y + -1x3 Add '-1y3' to each side of the equation. y3 + -1y3 = 6xy2 + 6x2y + -1x3 + -1y3 Combine like terms: y3 + -1y3 = 0 0 = 6xy2 + 6x2y + -1x3 + -1y3 Simplifying 0 = 6xy2 + 6x2y + -1x3 + -1y3 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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