(8xy-1)dx+(4x^2+1)dy=0

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Solution for (8xy-1)dx+(4x^2+1)dy=0 equation: 


Simplifying
(8xy + -1) * dx + (4x2 + 1) * dy = 0

Reorder the terms:
(-1 + 8xy) * dx + (4x2 + 1) * dy = 0

Reorder the terms for easier multiplication:
dx(-1 + 8xy) + (4x2 + 1) * dy = 0
(-1 * dx + 8xy * dx) + (4x2 + 1) * dy = 0
(-1dx + 8dx2y) + (4x2 + 1) * dy = 0

Reorder the terms:
-1dx + 8dx2y + (1 + 4x2) * dy = 0

Reorder the terms for easier multiplication:
-1dx + 8dx2y + dy(1 + 4x2) = 0
-1dx + 8dx2y + (1 * dy + 4x2 * dy) = 0

Reorder the terms:
-1dx + 8dx2y + (4dx2y + 1dy) = 0
-1dx + 8dx2y + (4dx2y + 1dy) = 0

Combine like terms: 8dx2y + 4dx2y = 12dx2y
-1dx + 12dx2y + 1dy = 0

Solving
-1dx + 12dx2y + 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(-1x + 12x2y + 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 '(-1x + 12x2y + y)' equal to zero and attempt to solve:

Simplifying
-1x + 12x2y + y = 0

Solving
-1x + 12x2y + y = 0

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

Add 'x' to each side of the equation.
-1x + 12x2y + x + y = 0 + x

Reorder the terms:
-1x + x + 12x2y + y = 0 + x

Combine like terms: -1x + x = 0
0 + 12x2y + y = 0 + x
12x2y + y = 0 + x
Remove the zero:
12x2y + y = x

Add '-12x2y' to each side of the equation.
12x2y + -12x2y + y = x + -12x2y

Combine like terms: 12x2y + -12x2y = 0
0 + y = x + -12x2y
y = x + -12x2y

Add '-1y' to each side of the equation.
y + -1y = x + -12x2y + -1y

Combine like terms: y + -1y = 0
0 = x + -12x2y + -1y

Simplifying
0 = x + -12x2y + -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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