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

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


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

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

Reorder the terms:
2dxy2 + dy3 + (x + y2) * dx = 0

Reorder the terms for easier multiplication:
2dxy2 + dy3 + dx(x + y2) = 0
2dxy2 + dy3 + (x * dx + y2 * dx) = 0

Reorder the terms:
2dxy2 + dy3 + (dxy2 + dx2) = 0
2dxy2 + dy3 + (dxy2 + dx2) = 0

Reorder the terms:
2dxy2 + dxy2 + dx2 + dy3 = 0

Combine like terms: 2dxy2 + dxy2 = 3dxy2
3dxy2 + dx2 + dy3 = 0

Solving
3dxy2 + dx2 + 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(3xy2 + x2 + 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 '(3xy2 + x2 + y3)' equal to zero and attempt to solve:

Simplifying
3xy2 + x2 + y3 = 0

Solving
3xy2 + x2 + y3 = 0

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

Add '-3xy2' to each side of the equation.
3xy2 + x2 + -3xy2 + y3 = 0 + -3xy2

Reorder the terms:
3xy2 + -3xy2 + x2 + y3 = 0 + -3xy2

Combine like terms: 3xy2 + -3xy2 = 0
0 + x2 + y3 = 0 + -3xy2
x2 + y3 = 0 + -3xy2
Remove the zero:
x2 + y3 = -3xy2

Add '-1x2' to each side of the equation.
x2 + -1x2 + y3 = -3xy2 + -1x2

Combine like terms: x2 + -1x2 = 0
0 + y3 = -3xy2 + -1x2
y3 = -3xy2 + -1x2

Add '-1y3' to each side of the equation.
y3 + -1y3 = -3xy2 + -1x2 + -1y3

Combine like terms: y3 + -1y3 = 0
0 = -3xy2 + -1x2 + -1y3

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