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

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


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

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

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

Reorder the terms:
(dxy + 2dx2 + dx3) + 2dy = 0
(dxy + 2dx2 + dx3) + 2dy = 0

Solving
dxy + 2dx2 + dx3 + 2dy = 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 + x3 + 2y) = 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 + x3 + 2y)' equal to zero and attempt to solve:

Simplifying
xy + 2x2 + x3 + 2y = 0

Solving
xy + 2x2 + x3 + 2y = 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 + x3 + -1xy + 2y = 0 + -1xy

Reorder the terms:
xy + -1xy + 2x2 + x3 + 2y = 0 + -1xy

Combine like terms: xy + -1xy = 0
0 + 2x2 + x3 + 2y = 0 + -1xy
2x2 + x3 + 2y = 0 + -1xy
Remove the zero:
2x2 + x3 + 2y = -1xy

Add '-2x2' to each side of the equation.
2x2 + x3 + -2x2 + 2y = -1xy + -2x2

Reorder the terms:
2x2 + -2x2 + x3 + 2y = -1xy + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + x3 + 2y = -1xy + -2x2
x3 + 2y = -1xy + -2x2

Add '-1x3' to each side of the equation.
x3 + -1x3 + 2y = -1xy + -2x2 + -1x3

Combine like terms: x3 + -1x3 = 0
0 + 2y = -1xy + -2x2 + -1x3
2y = -1xy + -2x2 + -1x3

Add '-2y' to each side of the equation.
2y + -2y = -1xy + -2x2 + -1x3 + -2y

Combine like terms: 2y + -2y = 0
0 = -1xy + -2x2 + -1x3 + -2y

Simplifying
0 = -1xy + -2x2 + -1x3 + -2y

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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