(x^3y^2+x)dx+(x^2y^3-y)dx=0

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Solution for (x^3y^2+x)dx+(x^2y^3-y)dx=0 equation:


Simplifying
(x3y2 + x) * dx + (x2y3 + -1y) * dx = 0

Reorder the terms:
(x + x3y2) * dx + (x2y3 + -1y) * dx = 0

Reorder the terms for easier multiplication:
dx(x + x3y2) + (x2y3 + -1y) * dx = 0
(x * dx + x3y2 * dx) + (x2y3 + -1y) * dx = 0
(dx2 + dx4y2) + (x2y3 + -1y) * dx = 0

Reorder the terms for easier multiplication:
dx2 + dx4y2 + dx(x2y3 + -1y) = 0
dx2 + dx4y2 + (x2y3 * dx + -1y * dx) = 0

Reorder the terms:
dx2 + dx4y2 + (-1dxy + dx3y3) = 0
dx2 + dx4y2 + (-1dxy + dx3y3) = 0

Reorder the terms:
-1dxy + dx2 + dx3y3 + dx4y2 = 0

Solving
-1dxy + dx2 + dx3y3 + dx4y2 = 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(-1y + x + x2y3 + x3y2) = 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 '(-1y + x + x2y3 + x3y2)' equal to zero and attempt to solve: Simplifying -1y + x + x2y3 + x3y2 = 0 Reorder the terms: x + x2y3 + x3y2 + -1y = 0 Solving x + x2y3 + x3y2 + -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 + x2y3 + x3y2 + -1x + -1y = 0 + -1x Reorder the terms: x + -1x + x2y3 + x3y2 + -1y = 0 + -1x Combine like terms: x + -1x = 0 0 + x2y3 + x3y2 + -1y = 0 + -1x x2y3 + x3y2 + -1y = 0 + -1x Remove the zero: x2y3 + x3y2 + -1y = -1x Add '-1x2y3' to each side of the equation. x2y3 + x3y2 + -1x2y3 + -1y = -1x + -1x2y3 Reorder the terms: x2y3 + -1x2y3 + x3y2 + -1y = -1x + -1x2y3 Combine like terms: x2y3 + -1x2y3 = 0 0 + x3y2 + -1y = -1x + -1x2y3 x3y2 + -1y = -1x + -1x2y3 Add '-1x3y2' to each side of the equation. x3y2 + -1x3y2 + -1y = -1x + -1x2y3 + -1x3y2 Combine like terms: x3y2 + -1x3y2 = 0 0 + -1y = -1x + -1x2y3 + -1x3y2 -1y = -1x + -1x2y3 + -1x3y2 Add 'y' to each side of the equation. -1y + y = -1x + -1x2y3 + -1x3y2 + y Combine like terms: -1y + y = 0 0 = -1x + -1x2y3 + -1x3y2 + y Simplifying 0 = -1x + -1x2y3 + -1x3y2 + y 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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