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

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


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

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

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

Multiply y * dx
2dxy(x + x2 + -1y) + (x2 + -2y) * dy = 0
(x * 2dxy + x2 * 2dxy + -1y * 2dxy) + (x2 + -2y) * dy = 0

Reorder the terms:
(-2dxy2 + 2dx2y + 2dx3y) + (x2 + -2y) * dy = 0
(-2dxy2 + 2dx2y + 2dx3y) + (x2 + -2y) * dy = 0

Reorder the terms for easier multiplication:
-2dxy2 + 2dx2y + 2dx3y + dy(x2 + -2y) = 0
-2dxy2 + 2dx2y + 2dx3y + (x2 * dy + -2y * dy) = 0
-2dxy2 + 2dx2y + 2dx3y + (dx2y + -2dy2) = 0

Reorder the terms:
-2dxy2 + 2dx2y + dx2y + 2dx3y + -2dy2 = 0

Combine like terms: 2dx2y + dx2y = 3dx2y
-2dxy2 + 3dx2y + 2dx3y + -2dy2 = 0

Solving
-2dxy2 + 3dx2y + 2dx3y + -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), 'dy'.
dy(-2xy + 3x2 + 2x3 + -2y) = 0


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

Simplifying
dy = 0

Solving
dy = 0

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

Simplifying
dy = 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 '(-2xy + 3x2 + 2x3 + -2y)' equal to zero and attempt to solve:

Simplifying
-2xy + 3x2 + 2x3 + -2y = 0

Solving
-2xy + 3x2 + 2x3 + -2y = 0

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

Add '2xy' to each side of the equation.
-2xy + 3x2 + 2x3 + 2xy + -2y = 0 + 2xy

Reorder the terms:
-2xy + 2xy + 3x2 + 2x3 + -2y = 0 + 2xy

Combine like terms: -2xy + 2xy = 0
0 + 3x2 + 2x3 + -2y = 0 + 2xy
3x2 + 2x3 + -2y = 0 + 2xy
Remove the zero:
3x2 + 2x3 + -2y = 2xy

Add '-3x2' to each side of the equation.
3x2 + 2x3 + -3x2 + -2y = 2xy + -3x2

Reorder the terms:
3x2 + -3x2 + 2x3 + -2y = 2xy + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + 2x3 + -2y = 2xy + -3x2
2x3 + -2y = 2xy + -3x2

Add '-2x3' to each side of the equation.
2x3 + -2x3 + -2y = 2xy + -3x2 + -2x3

Combine like terms: 2x3 + -2x3 = 0
0 + -2y = 2xy + -3x2 + -2x3
-2y = 2xy + -3x2 + -2x3

Add '2y' to each side of the equation.
-2y + 2y = 2xy + -3x2 + -2x3 + 2y

Combine like terms: -2y + 2y = 0
0 = 2xy + -3x2 + -2x3 + 2y

Simplifying
0 = 2xy + -3x2 + -2x3 + 2y

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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