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

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


Simplifying
(-4x2 + 2y) * dx + (2x + 4y) * dy = 0

Reorder the terms for easier multiplication:
dx(-4x2 + 2y) + (2x + 4y) * dy = 0
(-4x2 * dx + 2y * dx) + (2x + 4y) * dy = 0

Reorder the terms:
(2dxy + -4dx3) + (2x + 4y) * dy = 0
(2dxy + -4dx3) + (2x + 4y) * dy = 0

Reorder the terms for easier multiplication:
2dxy + -4dx3 + dy(2x + 4y) = 0
2dxy + -4dx3 + (2x * dy + 4y * dy) = 0
2dxy + -4dx3 + (2dxy + 4dy2) = 0

Reorder the terms:
2dxy + 2dxy + -4dx3 + 4dy2 = 0

Combine like terms: 2dxy + 2dxy = 4dxy
4dxy + -4dx3 + 4dy2 = 0

Solving
4dxy + -4dx3 + 4dy2 = 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), '4d'.
4d(xy + -1x3 + y2) = 0

Ignore the factor 4.

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 '(xy + -1x3 + y2)' equal to zero and attempt to solve:

Simplifying
xy + -1x3 + y2 = 0

Solving
xy + -1x3 + y2 = 0

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

Add '-1xy' to each side of the equation.
xy + -1x3 + -1xy + y2 = 0 + -1xy

Reorder the terms:
xy + -1xy + -1x3 + y2 = 0 + -1xy

Combine like terms: xy + -1xy = 0
0 + -1x3 + y2 = 0 + -1xy
-1x3 + y2 = 0 + -1xy
Remove the zero:
-1x3 + y2 = -1xy

Add 'x3' to each side of the equation.
-1x3 + x3 + y2 = -1xy + x3

Combine like terms: -1x3 + x3 = 0
0 + y2 = -1xy + x3
y2 = -1xy + x3

Add '-1y2' to each side of the equation.
y2 + -1y2 = -1xy + x3 + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -1xy + x3 + -1y2

Simplifying
0 = -1xy + x3 + -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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