(1+x^2)dy+(xy+x^3+x)dx=0

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Solution for (1+x^2)dy+(xy+x^3+x)dx=0 equation: 


Simplifying
(1 + x2) * dy + (xy + x3 + x) * dx = 0

Reorder the terms for easier multiplication:
dy(1 + x2) + (xy + x3 + x) * dx = 0
(1 * dy + x2 * dy) + (xy + x3 + x) * dx = 0

Reorder the terms:
(dx2y + 1dy) + (xy + x3 + x) * dx = 0
(dx2y + 1dy) + (xy + x3 + x) * dx = 0

Reorder the terms:
dx2y + 1dy + (x + xy + x3) * dx = 0

Reorder the terms for easier multiplication:
dx2y + 1dy + dx(x + xy + x3) = 0
dx2y + 1dy + (x * dx + xy * dx + x3 * dx) = 0
dx2y + 1dy + (dx2 + dx2y + dx4) = 0

Reorder the terms:
dx2 + dx2y + dx2y + dx4 + 1dy = 0

Combine like terms: dx2y + dx2y = 2dx2y
dx2 + 2dx2y + dx4 + 1dy = 0

Solving
dx2 + 2dx2y + dx4 + 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(x2 + 2x2y + x4 + 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 '(x2 + 2x2y + x4 + y)' equal to zero and attempt to solve:

Simplifying
x2 + 2x2y + x4 + y = 0

Solving
x2 + 2x2y + x4 + y = 0

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

Add '-1x2' to each side of the equation.
x2 + 2x2y + x4 + -1x2 + y = 0 + -1x2

Reorder the terms:
x2 + -1x2 + 2x2y + x4 + y = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
0 + 2x2y + x4 + y = 0 + -1x2
2x2y + x4 + y = 0 + -1x2
Remove the zero:
2x2y + x4 + y = -1x2

Add '-2x2y' to each side of the equation.
2x2y + x4 + -2x2y + y = -1x2 + -2x2y

Reorder the terms:
2x2y + -2x2y + x4 + y = -1x2 + -2x2y

Combine like terms: 2x2y + -2x2y = 0
0 + x4 + y = -1x2 + -2x2y
x4 + y = -1x2 + -2x2y

Add '-1x4' to each side of the equation.
x4 + -1x4 + y = -1x2 + -2x2y + -1x4

Combine like terms: x4 + -1x4 = 0
0 + y = -1x2 + -2x2y + -1x4
y = -1x2 + -2x2y + -1x4

Add '-1y' to each side of the equation.
y + -1y = -1x2 + -2x2y + -1x4 + -1y

Combine like terms: y + -1y = 0
0 = -1x2 + -2x2y + -1x4 + -1y

Simplifying
0 = -1x2 + -2x2y + -1x4 + -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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