(2xy+x^2+x^4)dx-(1+x^2)dy=0

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Solution for (2xy+x^2+x^4)dx-(1+x^2)dy=0 equation: 


Simplifying
(2xy + x2 + x4) * dx + -1(1 + x2) * dy = 0

Reorder the terms for easier multiplication:
dx(2xy + x2 + x4) + -1(1 + x2) * dy = 0
(2xy * dx + x2 * dx + x4 * dx) + -1(1 + x2) * dy = 0
(2dx2y + dx3 + dx5) + -1(1 + x2) * dy = 0

Reorder the terms for easier multiplication:
2dx2y + dx3 + dx5 + -1dy(1 + x2) = 0
2dx2y + dx3 + dx5 + (1 * -1dy + x2 * -1dy) = 0

Reorder the terms:
2dx2y + dx3 + dx5 + (-1dx2y + -1dy) = 0
2dx2y + dx3 + dx5 + (-1dx2y + -1dy) = 0

Reorder the terms:
2dx2y + -1dx2y + dx3 + dx5 + -1dy = 0

Combine like terms: 2dx2y + -1dx2y = 1dx2y
1dx2y + dx3 + dx5 + -1dy = 0

Solving
1dx2y + dx3 + dx5 + -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(x2y + x3 + x5 + -1y) = 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 '(x2y + x3 + x5 + -1y)' equal to zero and attempt to solve:

Simplifying
x2y + x3 + x5 + -1y = 0

Solving
x2y + x3 + x5 + -1y = 0

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

Add '-1x2y' to each side of the equation.
x2y + x3 + x5 + -1x2y + -1y = 0 + -1x2y

Reorder the terms:
x2y + -1x2y + x3 + x5 + -1y = 0 + -1x2y

Combine like terms: x2y + -1x2y = 0
0 + x3 + x5 + -1y = 0 + -1x2y
x3 + x5 + -1y = 0 + -1x2y
Remove the zero:
x3 + x5 + -1y = -1x2y

Add '-1x3' to each side of the equation.
x3 + x5 + -1x3 + -1y = -1x2y + -1x3

Reorder the terms:
x3 + -1x3 + x5 + -1y = -1x2y + -1x3

Combine like terms: x3 + -1x3 = 0
0 + x5 + -1y = -1x2y + -1x3
x5 + -1y = -1x2y + -1x3

Add '-1x5' to each side of the equation.
x5 + -1x5 + -1y = -1x2y + -1x3 + -1x5

Combine like terms: x5 + -1x5 = 0
0 + -1y = -1x2y + -1x3 + -1x5
-1y = -1x2y + -1x3 + -1x5

Add 'y' to each side of the equation.
-1y + y = -1x2y + -1x3 + -1x5 + y

Combine like terms: -1y + y = 0
0 = -1x2y + -1x3 + -1x5 + y

Simplifying
0 = -1x2y + -1x3 + -1x5 + y

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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