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

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


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

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

Multiply x * dx
2dx2(1 + y2) + -1y(1 + 2y2) * dy = 0
(1 * 2dx2 + y2 * 2dx2) + -1y(1 + 2y2) * dy = 0
(2dx2 + 2dx2y2) + -1y(1 + 2y2) * dy = 0

Reorder the terms for easier multiplication:
2dx2 + 2dx2y2 + -1y * dy(1 + 2y2) = 0

Multiply y * dy
2dx2 + 2dx2y2 + -1dy2(1 + 2y2) = 0
2dx2 + 2dx2y2 + (1 * -1dy2 + 2y2 * -1dy2) = 0
2dx2 + 2dx2y2 + (-1dy2 + -2dy4) = 0

Solving
2dx2 + 2dx2y2 + -1dy2 + -2dy4 = 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(2x2 + 2x2y2 + -1y2 + -2y4) = 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 '(2x2 + 2x2y2 + -1y2 + -2y4)' equal to zero and attempt to solve:

Simplifying
2x2 + 2x2y2 + -1y2 + -2y4 = 0

Solving
2x2 + 2x2y2 + -1y2 + -2y4 = 0

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

Add '-2x2' to each side of the equation.
2x2 + 2x2y2 + -1y2 + -2x2 + -2y4 = 0 + -2x2

Reorder the terms:
2x2 + -2x2 + 2x2y2 + -1y2 + -2y4 = 0 + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + 2x2y2 + -1y2 + -2y4 = 0 + -2x2
2x2y2 + -1y2 + -2y4 = 0 + -2x2
Remove the zero:
2x2y2 + -1y2 + -2y4 = -2x2

Add '-2x2y2' to each side of the equation.
2x2y2 + -1y2 + -2x2y2 + -2y4 = -2x2 + -2x2y2

Reorder the terms:
2x2y2 + -2x2y2 + -1y2 + -2y4 = -2x2 + -2x2y2

Combine like terms: 2x2y2 + -2x2y2 = 0
0 + -1y2 + -2y4 = -2x2 + -2x2y2
-1y2 + -2y4 = -2x2 + -2x2y2

Add 'y2' to each side of the equation.
-1y2 + y2 + -2y4 = -2x2 + -2x2y2 + y2

Combine like terms: -1y2 + y2 = 0
0 + -2y4 = -2x2 + -2x2y2 + y2
-2y4 = -2x2 + -2x2y2 + y2

Add '2y4' to each side of the equation.
-2y4 + 2y4 = -2x2 + -2x2y2 + y2 + 2y4

Combine like terms: -2y4 + 2y4 = 0
0 = -2x2 + -2x2y2 + y2 + 2y4

Simplifying
0 = -2x2 + -2x2y2 + y2 + 2y4

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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