y*dx+(x*y+x-3y)*dy=0

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Solution for y*dx+(x*y+x-3y)*dy=0 equation: 


Simplifying
y * dx + (x * y + x + -3y) * dy = 0

Multiply y * dx
dxy + (x * y + x + -3y) * dy = 0

Multiply x * y
dxy + (xy + x + -3y) * dy = 0

Reorder the terms:
dxy + (x + xy + -3y) * dy = 0

Reorder the terms for easier multiplication:
dxy + dy(x + xy + -3y) = 0
dxy + (x * dy + xy * dy + -3y * dy) = 0
dxy + (dxy + dxy2 + -3dy2) = 0

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

Solving
2dxy + dxy2 + -3dy2 = 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(2x + xy + -3y) = 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 '(2x + xy + -3y)' equal to zero and attempt to solve:

Simplifying
2x + xy + -3y = 0

Solving
2x + xy + -3y = 0

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

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

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

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

Add '-1xy' to each side of the equation.
xy + -1xy + -3y = -2x + -1xy

Combine like terms: xy + -1xy = 0
0 + -3y = -2x + -1xy
-3y = -2x + -1xy

Add '3y' to each side of the equation.
-3y + 3y = -2x + -1xy + 3y

Combine like terms: -3y + 3y = 0
0 = -2x + -1xy + 3y

Simplifying
0 = -2x + -1xy + 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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