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

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


Simplifying
x(y2 + 1) * dx + y(x2 + 1) * dy = 0

Reorder the terms:
x(1 + y2) * dx + y(x2 + 1) * dy = 0

Reorder the terms for easier multiplication:
x * dx(1 + y2) + y(x2 + 1) * dy = 0

Multiply x * dx
dx2(1 + y2) + y(x2 + 1) * dy = 0
(1 * dx2 + y2 * dx2) + y(x2 + 1) * dy = 0
(1dx2 + dx2y2) + y(x2 + 1) * dy = 0

Reorder the terms:
1dx2 + dx2y2 + y(1 + x2) * dy = 0

Reorder the terms for easier multiplication:
1dx2 + dx2y2 + y * dy(1 + x2) = 0

Multiply y * dy
1dx2 + dx2y2 + dy2(1 + x2) = 0
1dx2 + dx2y2 + (1 * dy2 + x2 * dy2) = 0

Reorder the terms:
1dx2 + dx2y2 + (dx2y2 + 1dy2) = 0
1dx2 + dx2y2 + (dx2y2 + 1dy2) = 0

Combine like terms: dx2y2 + dx2y2 = 2dx2y2
1dx2 + 2dx2y2 + 1dy2 = 0

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

Simplifying
x2 + 2x2y2 + y2 = 0

Solving
x2 + 2x2y2 + y2 = 0

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

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

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

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

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

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

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

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

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