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

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


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

Multiply y2 * x
(x + -1xy2) * dx + -1(y + -1(x2) * y) * dy = 0

Reorder the terms for easier multiplication:
dx(x + -1xy2) + -1(y + -1(x2) * y) * dy = 0
(x * dx + -1xy2 * dx) + -1(y + -1(x2) * y) * dy = 0
(dx2 + -1dx2y2) + -1(y + -1(x2) * y) * dy = 0

Multiply x2 * y
dx2 + -1dx2y2 + -1(y + -1x2y) * dy = 0

Reorder the terms:
dx2 + -1dx2y2 + -1(-1x2y + y) * dy = 0

Reorder the terms for easier multiplication:
dx2 + -1dx2y2 + -1dy(-1x2y + y) = 0
dx2 + -1dx2y2 + (-1x2y * -1dy + y * -1dy) = 0
dx2 + -1dx2y2 + (1dx2y2 + -1dy2) = 0

Combine like terms: -1dx2y2 + 1dx2y2 = 0
dx2 + 0 + -1dy2 = 0
dx2 + -1dy2 = 0

Solving
dx2 + -1dy2 = 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(x2 + -1y2) = 0

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

Subproblem 3

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