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

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


Simplifying
(xy + 2x + y + 2) * dx + (x2 + 2x) * dy = 0

Reorder the terms:
(2 + 2x + xy + y) * dx + (x2 + 2x) * dy = 0

Reorder the terms for easier multiplication:
dx(2 + 2x + xy + y) + (x2 + 2x) * dy = 0
(2 * dx + 2x * dx + xy * dx + y * dx) + (x2 + 2x) * dy = 0

Reorder the terms:
(2dx + dxy + 2dx2 + dx2y) + (x2 + 2x) * dy = 0
(2dx + dxy + 2dx2 + dx2y) + (x2 + 2x) * dy = 0

Reorder the terms:
2dx + dxy + 2dx2 + dx2y + (2x + x2) * dy = 0

Reorder the terms for easier multiplication:
2dx + dxy + 2dx2 + dx2y + dy(2x + x2) = 0
2dx + dxy + 2dx2 + dx2y + (2x * dy + x2 * dy) = 0
2dx + dxy + 2dx2 + dx2y + (2dxy + dx2y) = 0

Reorder the terms:
2dx + dxy + 2dxy + 2dx2 + dx2y + dx2y = 0

Combine like terms: dxy + 2dxy = 3dxy
2dx + 3dxy + 2dx2 + dx2y + dx2y = 0

Combine like terms: dx2y + dx2y = 2dx2y
2dx + 3dxy + 2dx2 + 2dx2y = 0

Solving
2dx + 3dxy + 2dx2 + 2dx2y = 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), 'dx'.
dx(2 + 3y + 2x + 2xy) = 0


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

Simplifying
dx = 0

Solving
dx = 0

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

Simplifying
dx = 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 '(2 + 3y + 2x + 2xy)' equal to zero and attempt to solve:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Simplifying
0 = -2 + -2x + -2xy + -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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