(2x+y)dx+(3y-1)dy=0

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Solution for (2x+y)dx+(3y-1)dy=0 equation: 


Simplifying
(2x + y) * dx + (3y + -1) * dy = 0

Reorder the terms for easier multiplication:
dx(2x + y) + (3y + -1) * dy = 0
(2x * dx + y * dx) + (3y + -1) * dy = 0

Reorder the terms:
(dxy + 2dx2) + (3y + -1) * dy = 0
(dxy + 2dx2) + (3y + -1) * dy = 0

Reorder the terms:
dxy + 2dx2 + (-1 + 3y) * dy = 0

Reorder the terms for easier multiplication:
dxy + 2dx2 + dy(-1 + 3y) = 0
dxy + 2dx2 + (-1 * dy + 3y * dy) = 0
dxy + 2dx2 + (-1dy + 3dy2) = 0

Solving
dxy + 2dx2 + -1dy + 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), 'd'.
d(xy + 2x2 + -1y + 3y2) = 0


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

Simplifying
d = 0

Solving
d = 0

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

Simplifying
d = 0

Subproblem 2
Set the factor '(xy + 2x2 + -1y + 3y2)' equal to zero and attempt to solve:

Simplifying
xy + 2x2 + -1y + 3y2 = 0

Solving
xy + 2x2 + -1y + 3y2 = 0

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

Add '-1xy' to each side of the equation.
xy + 2x2 + -1y + -1xy + 3y2 = 0 + -1xy

Reorder the terms:
xy + -1xy + 2x2 + -1y + 3y2 = 0 + -1xy

Combine like terms: xy + -1xy = 0
0 + 2x2 + -1y + 3y2 = 0 + -1xy
2x2 + -1y + 3y2 = 0 + -1xy
Remove the zero:
2x2 + -1y + 3y2 = -1xy

Add '-2x2' to each side of the equation.
2x2 + -1y + -2x2 + 3y2 = -1xy + -2x2

Reorder the terms:
2x2 + -2x2 + -1y + 3y2 = -1xy + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + -1y + 3y2 = -1xy + -2x2
-1y + 3y2 = -1xy + -2x2

Add 'y' to each side of the equation.
-1y + y + 3y2 = -1xy + -2x2 + y

Combine like terms: -1y + y = 0
0 + 3y2 = -1xy + -2x2 + y
3y2 = -1xy + -2x2 + y

Add '-3y2' to each side of the equation.
3y2 + -3y2 = -1xy + -2x2 + y + -3y2

Combine like terms: 3y2 + -3y2 = 0
0 = -1xy + -2x2 + y + -3y2

Simplifying
0 = -1xy + -2x2 + y + -3y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}

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