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

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


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

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

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

Reorder the terms for easier multiplication:
dx2 + 2dx2y + dy(x2 + 2y) = 0
dx2 + 2dx2y + (x2 * dy + 2y * dy) = 0
dx2 + 2dx2y + (dx2y + 2dy2) = 0

Combine like terms: 2dx2y + dx2y = 3dx2y
dx2 + 3dx2y + 2dy2 = 0

Solving
dx2 + 3dx2y + 2dy2 = 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(x2 + 3x2y + 2y2) = 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 '(x2 + 3x2y + 2y2)' equal to zero and attempt to solve:

Simplifying
x2 + 3x2y + 2y2 = 0

Solving
x2 + 3x2y + 2y2 = 0

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

Add '-1x2' to each side of the equation.
x2 + 3x2y + -1x2 + 2y2 = 0 + -1x2

Reorder the terms:
x2 + -1x2 + 3x2y + 2y2 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
0 + 3x2y + 2y2 = 0 + -1x2
3x2y + 2y2 = 0 + -1x2
Remove the zero:
3x2y + 2y2 = -1x2

Add '-3x2y' to each side of the equation.
3x2y + -3x2y + 2y2 = -1x2 + -3x2y

Combine like terms: 3x2y + -3x2y = 0
0 + 2y2 = -1x2 + -3x2y
2y2 = -1x2 + -3x2y

Add '-2y2' to each side of the equation.
2y2 + -2y2 = -1x2 + -3x2y + -2y2

Combine like terms: 2y2 + -2y2 = 0
0 = -1x2 + -3x2y + -2y2

Simplifying
0 = -1x2 + -3x2y + -2y2

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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