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

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


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

Multiply y * x2
(1 + -1x2y) * dx + x2(y + -1x) * dy = 0

Reorder the terms for easier multiplication:
dx(1 + -1x2y) + x2(y + -1x) * dy = 0
(1 * dx + -1x2y * dx) + x2(y + -1x) * dy = 0
(1dx + -1dx3y) + x2(y + -1x) * dy = 0

Reorder the terms:
1dx + -1dx3y + x2(-1x + y) * dy = 0

Reorder the terms for easier multiplication:
1dx + -1dx3y + x2 * dy(-1x + y) = 0

Multiply x2 * dy
1dx + -1dx3y + dx2y(-1x + y) = 0
1dx + -1dx3y + (-1x * dx2y + y * dx2y) = 0

Reorder the terms:
1dx + -1dx3y + (dx2y2 + -1dx3y) = 0
1dx + -1dx3y + (dx2y2 + -1dx3y) = 0

Reorder the terms:
1dx + dx2y2 + -1dx3y + -1dx3y = 0

Combine like terms: -1dx3y + -1dx3y = -2dx3y
1dx + dx2y2 + -2dx3y = 0

Solving
1dx + dx2y2 + -2dx3y = 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(1 + xy2 + -2x2y) = 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 '(1 + xy2 + -2x2y)' equal to zero and attempt to solve: Simplifying 1 + xy2 + -2x2y = 0 Solving 1 + xy2 + -2x2y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + xy2 + -1 + -2x2y = 0 + -1 Reorder the terms: 1 + -1 + xy2 + -2x2y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + xy2 + -2x2y = 0 + -1 xy2 + -2x2y = 0 + -1 Combine like terms: 0 + -1 = -1 xy2 + -2x2y = -1 Add '-1xy2' to each side of the equation. xy2 + -1xy2 + -2x2y = -1 + -1xy2 Combine like terms: xy2 + -1xy2 = 0 0 + -2x2y = -1 + -1xy2 -2x2y = -1 + -1xy2 Add '2x2y' to each side of the equation. -2x2y + 2x2y = -1 + -1xy2 + 2x2y Combine like terms: -2x2y + 2x2y = 0 0 = -1 + -1xy2 + 2x2y Simplifying 0 = -1 + -1xy2 + 2x2y 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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