y(x^3y^3+2x^2-y)dx+(x^4y^3-2x^3)dy=0

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Solution for y(x^3y^3+2x^2-y)dx+(x^4y^3-2x^3)dy=0 equation:


Simplifying
y(x3y3 + 2x2 + -1y) * dx + (x4y3 + -2x3) * dy = 0

Reorder the terms:
y(2x2 + x3y3 + -1y) * dx + (x4y3 + -2x3) * dy = 0

Reorder the terms for easier multiplication:
y * dx(2x2 + x3y3 + -1y) + (x4y3 + -2x3) * dy = 0

Multiply y * dx
dxy(2x2 + x3y3 + -1y) + (x4y3 + -2x3) * dy = 0
(2x2 * dxy + x3y3 * dxy + -1y * dxy) + (x4y3 + -2x3) * dy = 0

Reorder the terms:
(-1dxy2 + 2dx3y + dx4y4) + (x4y3 + -2x3) * dy = 0
(-1dxy2 + 2dx3y + dx4y4) + (x4y3 + -2x3) * dy = 0

Reorder the terms:
-1dxy2 + 2dx3y + dx4y4 + (-2x3 + x4y3) * dy = 0

Reorder the terms for easier multiplication:
-1dxy2 + 2dx3y + dx4y4 + dy(-2x3 + x4y3) = 0
-1dxy2 + 2dx3y + dx4y4 + (-2x3 * dy + x4y3 * dy) = 0
-1dxy2 + 2dx3y + dx4y4 + (-2dx3y + dx4y4) = 0

Reorder the terms:
-1dxy2 + 2dx3y + -2dx3y + dx4y4 + dx4y4 = 0

Combine like terms: 2dx3y + -2dx3y = 0
-1dxy2 + 0 + dx4y4 + dx4y4 = 0
-1dxy2 + dx4y4 + dx4y4 = 0

Combine like terms: dx4y4 + dx4y4 = 2dx4y4
-1dxy2 + 2dx4y4 = 0

Solving
-1dxy2 + 2dx4y4 = 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), 'dxy2'.
dxy2(-1 + 2x3y2) = 0

Subproblem 1

Set the factor 'dxy2' equal to zero and attempt to solve: Simplifying dxy2 = 0 Solving dxy2 = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dxy2 = 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 + 2x3y2)' equal to zero and attempt to solve: Simplifying -1 + 2x3y2 = 0 Solving -1 + 2x3y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 2x3y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2x3y2 = 0 + 1 2x3y2 = 0 + 1 Combine like terms: 0 + 1 = 1 2x3y2 = 1 Add '-2x3y2' to each side of the equation. 2x3y2 + -2x3y2 = 1 + -2x3y2 Combine like terms: 2x3y2 + -2x3y2 = 0 0 = 1 + -2x3y2 Simplifying 0 = 1 + -2x3y2 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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