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

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


Simplifying
(x2 + 2xy) * dx + (y2 + 2xy) * dy = 0

Reorder the terms:
(2xy + x2) * dx + (y2 + 2xy) * dy = 0

Reorder the terms for easier multiplication:
dx(2xy + x2) + (y2 + 2xy) * dy = 0
(2xy * dx + x2 * dx) + (y2 + 2xy) * dy = 0
(2dx2y + dx3) + (y2 + 2xy) * dy = 0

Reorder the terms:
2dx2y + dx3 + (2xy + y2) * dy = 0

Reorder the terms for easier multiplication:
2dx2y + dx3 + dy(2xy + y2) = 0
2dx2y + dx3 + (2xy * dy + y2 * dy) = 0
2dx2y + dx3 + (2dxy2 + dy3) = 0

Reorder the terms:
2dxy2 + 2dx2y + dx3 + dy3 = 0

Solving
2dxy2 + 2dx2y + dx3 + dy3 = 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(2xy2 + 2x2y + x3 + y3) = 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 '(2xy2 + 2x2y + x3 + y3)' equal to zero and attempt to solve:

Simplifying
2xy2 + 2x2y + x3 + y3 = 0

Solving
2xy2 + 2x2y + x3 + y3 = 0

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

Add '-2xy2' to each side of the equation.
2xy2 + 2x2y + x3 + -2xy2 + y3 = 0 + -2xy2

Reorder the terms:
2xy2 + -2xy2 + 2x2y + x3 + y3 = 0 + -2xy2

Combine like terms: 2xy2 + -2xy2 = 0
0 + 2x2y + x3 + y3 = 0 + -2xy2
2x2y + x3 + y3 = 0 + -2xy2
Remove the zero:
2x2y + x3 + y3 = -2xy2

Add '-2x2y' to each side of the equation.
2x2y + x3 + -2x2y + y3 = -2xy2 + -2x2y

Reorder the terms:
2x2y + -2x2y + x3 + y3 = -2xy2 + -2x2y

Combine like terms: 2x2y + -2x2y = 0
0 + x3 + y3 = -2xy2 + -2x2y
x3 + y3 = -2xy2 + -2x2y

Add '-1x3' to each side of the equation.
x3 + -1x3 + y3 = -2xy2 + -2x2y + -1x3

Combine like terms: x3 + -1x3 = 0
0 + y3 = -2xy2 + -2x2y + -1x3
y3 = -2xy2 + -2x2y + -1x3

Add '-1y3' to each side of the equation.
y3 + -1y3 = -2xy2 + -2x2y + -1x3 + -1y3

Combine like terms: y3 + -1y3 = 0
0 = -2xy2 + -2x2y + -1x3 + -1y3

Simplifying
0 = -2xy2 + -2x2y + -1x3 + -1y3

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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