(2xy+3y^2)dx+(x^2+6xy-2y)dy=0

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Solution for (2xy+3y^2)dx+(x^2+6xy-2y)dy=0 equation: 


Simplifying
(2xy + 3y2) * dx + (x2 + 6xy + -2y) * dy = 0

Reorder the terms for easier multiplication:
dx(2xy + 3y2) + (x2 + 6xy + -2y) * dy = 0
(2xy * dx + 3y2 * dx) + (x2 + 6xy + -2y) * dy = 0

Reorder the terms:
(3dxy2 + 2dx2y) + (x2 + 6xy + -2y) * dy = 0
(3dxy2 + 2dx2y) + (x2 + 6xy + -2y) * dy = 0

Reorder the terms:
3dxy2 + 2dx2y + (6xy + x2 + -2y) * dy = 0

Reorder the terms for easier multiplication:
3dxy2 + 2dx2y + dy(6xy + x2 + -2y) = 0
3dxy2 + 2dx2y + (6xy * dy + x2 * dy + -2y * dy) = 0
3dxy2 + 2dx2y + (6dxy2 + dx2y + -2dy2) = 0

Reorder the terms:
3dxy2 + 6dxy2 + 2dx2y + dx2y + -2dy2 = 0

Combine like terms: 3dxy2 + 6dxy2 = 9dxy2
9dxy2 + 2dx2y + dx2y + -2dy2 = 0

Combine like terms: 2dx2y + dx2y = 3dx2y
9dxy2 + 3dx2y + -2dy2 = 0

Solving
9dxy2 + 3dx2y + -2dy2 = 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), 'dy'.
dy(9xy + 3x2 + -2y) = 0


Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve:

Simplifying
dy = 0

Solving
dy = 0

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

Simplifying
dy = 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 '(9xy + 3x2 + -2y)' equal to zero and attempt to solve:

Simplifying
9xy + 3x2 + -2y = 0

Solving
9xy + 3x2 + -2y = 0

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

Add '-9xy' to each side of the equation.
9xy + 3x2 + -9xy + -2y = 0 + -9xy

Reorder the terms:
9xy + -9xy + 3x2 + -2y = 0 + -9xy

Combine like terms: 9xy + -9xy = 0
0 + 3x2 + -2y = 0 + -9xy
3x2 + -2y = 0 + -9xy
Remove the zero:
3x2 + -2y = -9xy

Add '-3x2' to each side of the equation.
3x2 + -3x2 + -2y = -9xy + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + -2y = -9xy + -3x2
-2y = -9xy + -3x2

Add '2y' to each side of the equation.
-2y + 2y = -9xy + -3x2 + 2y

Combine like terms: -2y + 2y = 0
0 = -9xy + -3x2 + 2y

Simplifying
0 = -9xy + -3x2 + 2y

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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