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

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


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

Reorder the terms:
(3 + X + -1y) * dx + (3x + y + 1) * dy = 0

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

Reorder the terms:
3dx + dxX + -1dxy + (1 + 3x + y) * dy = 0

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

Reorder the terms:
3dx + dxX + -1dxy + (3dxy + 1dy + dy2) = 0
3dx + dxX + -1dxy + (3dxy + 1dy + dy2) = 0

Combine like terms: -1dxy + 3dxy = 2dxy
3dx + dxX + 2dxy + 1dy + dy2 = 0

Solving
3dx + dxX + 2dxy + 1dy + dy2 = 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 + xX + 2xy + y + y2) = 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 + xX + 2xy + y + y2)' equal to zero and attempt to solve:

Simplifying
3x + xX + 2xy + y + y2 = 0

Solving
3x + xX + 2xy + y + y2 = 0

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

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

Reorder the terms:
3x + -3x + xX + 2xy + y + y2 = 0 + -3x

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

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

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

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

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

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

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

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

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

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

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

Simplifying
0 = -3x + -1xX + -2xy + -1y + -1y2

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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