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

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


Simplifying
int((-2xy2) + -3y) * dx + ((-2x2) * y + -3x) * dy = 0

Reorder the terms for easier multiplication:
int * dx((-2xy2) + -3y) + ((-2x2) * y + -3x) * dy = 0

Multiply int * dx
dintx((-2xy2) + -3y) + ((-2x2) * y + -3x) * dy = 0
((-2xy2) * dintx + -3y * dintx) + ((-2x2) * y + -3x) * dy = 0

Reorder the terms:
(-3dintxy + -2dintx2y2) + ((-2x2) * y + -3x) * dy = 0
(-3dintxy + -2dintx2y2) + ((-2x2) * y + -3x) * dy = 0

Remove parenthesis around (-2x2)
-3dintxy + -2dintx2y2 + (-2x2 * y + -3x) * dy = 0

Multiply x2 * y
-3dintxy + -2dintx2y2 + (-2x2y + -3x) * dy = 0

Reorder the terms:
-3dintxy + -2dintx2y2 + (-3x + -2x2y) * dy = 0

Reorder the terms for easier multiplication:
-3dintxy + -2dintx2y2 + dy(-3x + -2x2y) = 0
-3dintxy + -2dintx2y2 + (-3x * dy + -2x2y * dy) = 0
-3dintxy + -2dintx2y2 + (-3dxy + -2dx2y2) = 0

Solving
-3dintxy + -2dintx2y2 + -3dxy + -2dx2y2 = 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), '-1dxy'.
-1dxy(3int + 2intxy + 3 + 2xy) = 0

Ignore the factor -1.

Subproblem 1

Set the factor 'dxy' equal to zero and attempt to solve: Simplifying dxy = 0 Solving dxy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dxy = 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 '(3int + 2intxy + 3 + 2xy)' equal to zero and attempt to solve: Simplifying 3int + 2intxy + 3 + 2xy = 0 Reorder the terms: 3 + 3int + 2intxy + 2xy = 0 Solving 3 + 3int + 2intxy + 2xy = 0 Move all terms containing d to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + 3int + 2intxy + -3 + 2xy = 0 + -3 Reorder the terms: 3 + -3 + 3int + 2intxy + 2xy = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 3int + 2intxy + 2xy = 0 + -3 3int + 2intxy + 2xy = 0 + -3 Combine like terms: 0 + -3 = -3 3int + 2intxy + 2xy = -3 Add '-3int' to each side of the equation. 3int + 2intxy + -3int + 2xy = -3 + -3int Reorder the terms: 3int + -3int + 2intxy + 2xy = -3 + -3int Combine like terms: 3int + -3int = 0 0 + 2intxy + 2xy = -3 + -3int 2intxy + 2xy = -3 + -3int Add '-2intxy' to each side of the equation. 2intxy + -2intxy + 2xy = -3 + -3int + -2intxy Combine like terms: 2intxy + -2intxy = 0 0 + 2xy = -3 + -3int + -2intxy 2xy = -3 + -3int + -2intxy Add '-2xy' to each side of the equation. 2xy + -2xy = -3 + -3int + -2intxy + -2xy Combine like terms: 2xy + -2xy = 0 0 = -3 + -3int + -2intxy + -2xy Simplifying 0 = -3 + -3int + -2intxy + -2xy 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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