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

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


Simplifying
(6xy + y2) * dx + (3x2 + 2xy + -1y2) * dy = 0

Reorder the terms for easier multiplication:
dx(6xy + y2) + (3x2 + 2xy + -1y2) * dy = 0
(6xy * dx + y2 * dx) + (3x2 + 2xy + -1y2) * dy = 0

Reorder the terms:
(dxy2 + 6dx2y) + (3x2 + 2xy + -1y2) * dy = 0
(dxy2 + 6dx2y) + (3x2 + 2xy + -1y2) * dy = 0

Reorder the terms:
dxy2 + 6dx2y + (2xy + 3x2 + -1y2) * dy = 0

Reorder the terms for easier multiplication:
dxy2 + 6dx2y + dy(2xy + 3x2 + -1y2) = 0
dxy2 + 6dx2y + (2xy * dy + 3x2 * dy + -1y2 * dy) = 0
dxy2 + 6dx2y + (2dxy2 + 3dx2y + -1dy3) = 0

Reorder the terms:
dxy2 + 2dxy2 + 6dx2y + 3dx2y + -1dy3 = 0

Combine like terms: dxy2 + 2dxy2 = 3dxy2
3dxy2 + 6dx2y + 3dx2y + -1dy3 = 0

Combine like terms: 6dx2y + 3dx2y = 9dx2y
3dxy2 + 9dx2y + -1dy3 = 0

Solving
3dxy2 + 9dx2y + -1dy3 = 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(3xy + 9x2 + -1y2) = 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 '(3xy + 9x2 + -1y2)' equal to zero and attempt to solve:

Simplifying
3xy + 9x2 + -1y2 = 0

Solving
3xy + 9x2 + -1y2 = 0

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

Add '-3xy' to each side of the equation.
3xy + 9x2 + -3xy + -1y2 = 0 + -3xy

Reorder the terms:
3xy + -3xy + 9x2 + -1y2 = 0 + -3xy

Combine like terms: 3xy + -3xy = 0
0 + 9x2 + -1y2 = 0 + -3xy
9x2 + -1y2 = 0 + -3xy
Remove the zero:
9x2 + -1y2 = -3xy

Add '-9x2' to each side of the equation.
9x2 + -9x2 + -1y2 = -3xy + -9x2

Combine like terms: 9x2 + -9x2 = 0
0 + -1y2 = -3xy + -9x2
-1y2 = -3xy + -9x2

Add 'y2' to each side of the equation.
-1y2 + y2 = -3xy + -9x2 + y2

Combine like terms: -1y2 + y2 = 0
0 = -3xy + -9x2 + y2

Simplifying
0 = -3xy + -9x2 + y2

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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