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

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


Simplifying
(1 + x2) * dy + x(1 + 4y2) * dx = 0

Reorder the terms for easier multiplication:
dy(1 + x2) + x(1 + 4y2) * dx = 0
(1 * dy + x2 * dy) + x(1 + 4y2) * dx = 0

Reorder the terms:
(dx2y + 1dy) + x(1 + 4y2) * dx = 0
(dx2y + 1dy) + x(1 + 4y2) * dx = 0

Reorder the terms for easier multiplication:
dx2y + 1dy + x * dx(1 + 4y2) = 0

Multiply x * dx
dx2y + 1dy + dx2(1 + 4y2) = 0
dx2y + 1dy + (1 * dx2 + 4y2 * dx2) = 0
dx2y + 1dy + (1dx2 + 4dx2y2) = 0

Reorder the terms:
1dx2 + dx2y + 4dx2y2 + 1dy = 0

Solving
1dx2 + dx2y + 4dx2y2 + 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 + x2y + 4x2y2 + 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 + x2y + 4x2y2 + y)' equal to zero and attempt to solve:

Simplifying
x2 + x2y + 4x2y2 + y = 0

Solving
x2 + x2y + 4x2y2 + 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 + x2y + 4x2y2 + -1x2 + y = 0 + -1x2

Reorder the terms:
x2 + -1x2 + x2y + 4x2y2 + y = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
0 + x2y + 4x2y2 + y = 0 + -1x2
x2y + 4x2y2 + y = 0 + -1x2
Remove the zero:
x2y + 4x2y2 + y = -1x2

Add '-1x2y' to each side of the equation.
x2y + 4x2y2 + -1x2y + y = -1x2 + -1x2y

Reorder the terms:
x2y + -1x2y + 4x2y2 + y = -1x2 + -1x2y

Combine like terms: x2y + -1x2y = 0
0 + 4x2y2 + y = -1x2 + -1x2y
4x2y2 + y = -1x2 + -1x2y

Add '-4x2y2' to each side of the equation.
4x2y2 + -4x2y2 + y = -1x2 + -1x2y + -4x2y2

Combine like terms: 4x2y2 + -4x2y2 = 0
0 + y = -1x2 + -1x2y + -4x2y2
y = -1x2 + -1x2y + -4x2y2

Add '-1y' to each side of the equation.
y + -1y = -1x2 + -1x2y + -4x2y2 + -1y

Combine like terms: y + -1y = 0
0 = -1x2 + -1x2y + -4x2y2 + -1y

Simplifying
0 = -1x2 + -1x2y + -4x2y2 + -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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