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

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


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

Reorder the terms for easier multiplication:
dy(2xy + y) = (x + -1y2) * dx
(2xy * dy + y * dy) = (x + -1y2) * dx
(2dxy2 + dy2) = (x + -1y2) * dx

Reorder the terms for easier multiplication:
2dxy2 + dy2 = dx(x + -1y2)
2dxy2 + dy2 = (x * dx + -1y2 * dx)

Reorder the terms:
2dxy2 + dy2 = (-1dxy2 + dx2)
2dxy2 + dy2 = (-1dxy2 + dx2)

Solving
2dxy2 + dy2 = -1dxy2 + dx2

Solving for variable 'd'.

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

Add 'dxy2' to each side of the equation.
2dxy2 + dxy2 + dy2 = -1dxy2 + dxy2 + dx2

Combine like terms: 2dxy2 + dxy2 = 3dxy2
3dxy2 + dy2 = -1dxy2 + dxy2 + dx2

Combine like terms: -1dxy2 + dxy2 = 0
3dxy2 + dy2 = 0 + dx2
3dxy2 + dy2 = dx2

Add '-1dx2' to each side of the equation.
3dxy2 + -1dx2 + dy2 = dx2 + -1dx2

Combine like terms: dx2 + -1dx2 = 0
3dxy2 + -1dx2 + dy2 = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(3xy2 + -1x2 + 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 '(3xy2 + -1x2 + y2)' equal to zero and attempt to solve:

Simplifying
3xy2 + -1x2 + y2 = 0

Solving
3xy2 + -1x2 + y2 = 0

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

Add '-3xy2' to each side of the equation.
3xy2 + -1x2 + -3xy2 + y2 = 0 + -3xy2

Reorder the terms:
3xy2 + -3xy2 + -1x2 + y2 = 0 + -3xy2

Combine like terms: 3xy2 + -3xy2 = 0
0 + -1x2 + y2 = 0 + -3xy2
-1x2 + y2 = 0 + -3xy2
Remove the zero:
-1x2 + y2 = -3xy2

Add 'x2' to each side of the equation.
-1x2 + x2 + y2 = -3xy2 + x2

Combine like terms: -1x2 + x2 = 0
0 + y2 = -3xy2 + x2
y2 = -3xy2 + x2

Add '-1y2' to each side of the equation.
y2 + -1y2 = -3xy2 + x2 + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -3xy2 + x2 + -1y2

Simplifying
0 = -3xy2 + x2 + -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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