(Y^2+3)dx+(2xy-4)dy=0

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Solution for (Y^2+3)dx+(2xy-4)dy=0 equation: 


Simplifying
(Y2 + 3) * dx + (2xy + -4) * dy = 0

Reorder the terms:
(3 + Y2) * dx + (2xy + -4) * dy = 0

Reorder the terms for easier multiplication:
dx(3 + Y2) + (2xy + -4) * dy = 0
(3 * dx + Y2 * dx) + (2xy + -4) * dy = 0
(3dx + dxY2) + (2xy + -4) * dy = 0

Reorder the terms:
3dx + dxY2 + (-4 + 2xy) * dy = 0

Reorder the terms for easier multiplication:
3dx + dxY2 + dy(-4 + 2xy) = 0
3dx + dxY2 + (-4 * dy + 2xy * dy) = 0

Reorder the terms:
3dx + dxY2 + (2dxy2 + -4dy) = 0
3dx + dxY2 + (2dxy2 + -4dy) = 0

Solving
3dx + dxY2 + 2dxy2 + -4dy = 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(3x + xY2 + 2xy2 + -4y) = 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 '(3x + xY2 + 2xy2 + -4y)' equal to zero and attempt to solve:

Simplifying
3x + xY2 + 2xy2 + -4y = 0

Solving
3x + xY2 + 2xy2 + -4y = 0

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

Add '-3x' to each side of the equation.
3x + xY2 + 2xy2 + -3x + -4y = 0 + -3x

Reorder the terms:
3x + -3x + xY2 + 2xy2 + -4y = 0 + -3x

Combine like terms: 3x + -3x = 0
0 + xY2 + 2xy2 + -4y = 0 + -3x
xY2 + 2xy2 + -4y = 0 + -3x
Remove the zero:
xY2 + 2xy2 + -4y = -3x

Add '-1xY2' to each side of the equation.
xY2 + 2xy2 + -1xY2 + -4y = -3x + -1xY2

Reorder the terms:
xY2 + -1xY2 + 2xy2 + -4y = -3x + -1xY2

Combine like terms: xY2 + -1xY2 = 0
0 + 2xy2 + -4y = -3x + -1xY2
2xy2 + -4y = -3x + -1xY2

Add '-2xy2' to each side of the equation.
2xy2 + -2xy2 + -4y = -3x + -1xY2 + -2xy2

Combine like terms: 2xy2 + -2xy2 = 0
0 + -4y = -3x + -1xY2 + -2xy2
-4y = -3x + -1xY2 + -2xy2

Add '4y' to each side of the equation.
-4y + 4y = -3x + -1xY2 + -2xy2 + 4y

Combine like terms: -4y + 4y = 0
0 = -3x + -1xY2 + -2xy2 + 4y

Simplifying
0 = -3x + -1xY2 + -2xy2 + 4y

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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