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

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


Simplifying
(2xy + 3y2) + -1(2xy + x2) * dy = 0

Remove parenthesis around (2xy + 3y2)
2xy + 3y2 + -1(2xy + x2) * dy = 0

Reorder the terms for easier multiplication:
2xy + 3y2 + -1dy(2xy + x2) = 0
2xy + 3y2 + (2xy * -1dy + x2 * -1dy) = 0
2xy + 3y2 + (-2dxy2 + -1dx2y) = 0

Reorder the terms:
-2dxy2 + -1dx2y + 2xy + 3y2 = 0

Solving
-2dxy2 + -1dx2y + 2xy + 3y2 = 0

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '-2xy' to each side of the equation.
-2dxy2 + -1dx2y + 2xy + -2xy + 3y2 = 0 + -2xy

Combine like terms: 2xy + -2xy = 0
-2dxy2 + -1dx2y + 0 + 3y2 = 0 + -2xy
-2dxy2 + -1dx2y + 3y2 = 0 + -2xy
Remove the zero:
-2dxy2 + -1dx2y + 3y2 = -2xy

Add '-3y2' to each side of the equation.
-2dxy2 + -1dx2y + 3y2 + -3y2 = -2xy + -3y2

Combine like terms: 3y2 + -3y2 = 0
-2dxy2 + -1dx2y + 0 = -2xy + -3y2
-2dxy2 + -1dx2y = -2xy + -3y2

Reorder the terms:
-2dxy2 + -1dx2y + 2xy + 3y2 = -2xy + 2xy + -3y2 + 3y2

Combine like terms: -2xy + 2xy = 0
-2dxy2 + -1dx2y + 2xy + 3y2 = 0 + -3y2 + 3y2
-2dxy2 + -1dx2y + 2xy + 3y2 = -3y2 + 3y2

Combine like terms: -3y2 + 3y2 = 0
-2dxy2 + -1dx2y + 2xy + 3y2 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(-2dxy + -1dx2 + 2x + 3y) = 0

Subproblem 1

Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1y' to each side of the equation. y + -1y = 0 + -1y Remove the zero: 0 = -1y Simplifying 0 = -1y 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 '(-2dxy + -1dx2 + 2x + 3y)' equal to zero and attempt to solve: Simplifying -2dxy + -1dx2 + 2x + 3y = 0 Solving -2dxy + -1dx2 + 2x + 3y = 0 Move all terms containing d to the left, all other terms to the right. Add '-2x' to each side of the equation. -2dxy + -1dx2 + 2x + -2x + 3y = 0 + -2x Combine like terms: 2x + -2x = 0 -2dxy + -1dx2 + 0 + 3y = 0 + -2x -2dxy + -1dx2 + 3y = 0 + -2x Remove the zero: -2dxy + -1dx2 + 3y = -2x Add '-3y' to each side of the equation. -2dxy + -1dx2 + 3y + -3y = -2x + -3y Combine like terms: 3y + -3y = 0 -2dxy + -1dx2 + 0 = -2x + -3y -2dxy + -1dx2 = -2x + -3y 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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