x(y+2)dx+y(x^2+1)dy=0

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


Simplifying
x(y + 2) * dx + y(x2 + 1) * dy = 0

Reorder the terms:
x(2 + y) * dx + y(x2 + 1) * dy = 0

Reorder the terms for easier multiplication:
x * dx(2 + y) + y(x2 + 1) * dy = 0

Multiply x * dx
dx2(2 + y) + y(x2 + 1) * dy = 0
(2 * dx2 + y * dx2) + y(x2 + 1) * dy = 0
(2dx2 + dx2y) + y(x2 + 1) * dy = 0

Reorder the terms:
2dx2 + dx2y + y(1 + x2) * dy = 0

Reorder the terms for easier multiplication:
2dx2 + dx2y + y * dy(1 + x2) = 0

Multiply y * dy
2dx2 + dx2y + dy2(1 + x2) = 0
2dx2 + dx2y + (1 * dy2 + x2 * dy2) = 0

Reorder the terms:
2dx2 + dx2y + (dx2y2 + 1dy2) = 0
2dx2 + dx2y + (dx2y2 + 1dy2) = 0

Solving
2dx2 + dx2y + dx2y2 + 1dy2 = 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(2x2 + x2y + x2y2 + 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 '(2x2 + x2y + x2y2 + y2)' equal to zero and attempt to solve:

Simplifying
2x2 + x2y + x2y2 + y2 = 0

Solving
2x2 + x2y + x2y2 + y2 = 0

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

Add '-2x2' to each side of the equation.
2x2 + x2y + x2y2 + -2x2 + y2 = 0 + -2x2

Reorder the terms:
2x2 + -2x2 + x2y + x2y2 + y2 = 0 + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + x2y + x2y2 + y2 = 0 + -2x2
x2y + x2y2 + y2 = 0 + -2x2
Remove the zero:
x2y + x2y2 + y2 = -2x2

Add '-1x2y' to each side of the equation.
x2y + x2y2 + -1x2y + y2 = -2x2 + -1x2y

Reorder the terms:
x2y + -1x2y + x2y2 + y2 = -2x2 + -1x2y

Combine like terms: x2y + -1x2y = 0
0 + x2y2 + y2 = -2x2 + -1x2y
x2y2 + y2 = -2x2 + -1x2y

Add '-1x2y2' to each side of the equation.
x2y2 + -1x2y2 + y2 = -2x2 + -1x2y + -1x2y2

Combine like terms: x2y2 + -1x2y2 = 0
0 + y2 = -2x2 + -1x2y + -1x2y2
y2 = -2x2 + -1x2y + -1x2y2

Add '-1y2' to each side of the equation.
y2 + -1y2 = -2x2 + -1x2y + -1x2y2 + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -2x2 + -1x2y + -1x2y2 + -1y2

Simplifying
0 = -2x2 + -1x2y + -1x2y2 + -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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