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

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


Simplifying
((y2) + -2x) * dx + (2xy + 1) * dy = 0
(y2 + -2x) * dx + (2xy + 1) * dy = 0

Reorder the terms:
(-2x + y2) * dx + (2xy + 1) * dy = 0

Reorder the terms for easier multiplication:
dx(-2x + y2) + (2xy + 1) * dy = 0
(-2x * dx + y2 * dx) + (2xy + 1) * dy = 0

Reorder the terms:
(dxy2 + -2dx2) + (2xy + 1) * dy = 0
(dxy2 + -2dx2) + (2xy + 1) * dy = 0

Reorder the terms:
dxy2 + -2dx2 + (1 + 2xy) * dy = 0

Reorder the terms for easier multiplication:
dxy2 + -2dx2 + dy(1 + 2xy) = 0
dxy2 + -2dx2 + (1 * dy + 2xy * dy) = 0

Reorder the terms:
dxy2 + -2dx2 + (2dxy2 + 1dy) = 0
dxy2 + -2dx2 + (2dxy2 + 1dy) = 0

Reorder the terms:
dxy2 + 2dxy2 + -2dx2 + 1dy = 0

Combine like terms: dxy2 + 2dxy2 = 3dxy2
3dxy2 + -2dx2 + 1dy = 0

Solving
3dxy2 + -2dx2 + 1dy = 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(3xy2 + -2x2 + y) = 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 '(3xy2 + -2x2 + y)' equal to zero and attempt to solve:

Simplifying
3xy2 + -2x2 + y = 0

Solving
3xy2 + -2x2 + y = 0

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

Add '-3xy2' to each side of the equation.
3xy2 + -2x2 + -3xy2 + y = 0 + -3xy2

Reorder the terms:
3xy2 + -3xy2 + -2x2 + y = 0 + -3xy2

Combine like terms: 3xy2 + -3xy2 = 0
0 + -2x2 + y = 0 + -3xy2
-2x2 + y = 0 + -3xy2
Remove the zero:
-2x2 + y = -3xy2

Add '2x2' to each side of the equation.
-2x2 + 2x2 + y = -3xy2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
0 + y = -3xy2 + 2x2
y = -3xy2 + 2x2

Add '-1y' to each side of the equation.
y + -1y = -3xy2 + 2x2 + -1y

Combine like terms: y + -1y = 0
0 = -3xy2 + 2x2 + -1y

Simplifying
0 = -3xy2 + 2x2 + -1y

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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