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

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


Simplifying
(4x2 + -1y) * dx + (-1x + -2y) * dy = 0

Reorder the terms for easier multiplication:
dx(4x2 + -1y) + (-1x + -2y) * dy = 0
(4x2 * dx + -1y * dx) + (-1x + -2y) * dy = 0

Reorder the terms:
(-1dxy + 4dx3) + (-1x + -2y) * dy = 0
(-1dxy + 4dx3) + (-1x + -2y) * dy = 0

Reorder the terms for easier multiplication:
-1dxy + 4dx3 + dy(-1x + -2y) = 0
-1dxy + 4dx3 + (-1x * dy + -2y * dy) = 0
-1dxy + 4dx3 + (-1dxy + -2dy2) = 0

Reorder the terms:
-1dxy + -1dxy + 4dx3 + -2dy2 = 0

Combine like terms: -1dxy + -1dxy = -2dxy
-2dxy + 4dx3 + -2dy2 = 0

Solving
-2dxy + 4dx3 + -2dy2 = 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), '2d'.
2d(-1xy + 2x3 + -1y2) = 0

Ignore the factor 2.

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 '(-1xy + 2x3 + -1y2)' equal to zero and attempt to solve:

Simplifying
-1xy + 2x3 + -1y2 = 0

Solving
-1xy + 2x3 + -1y2 = 0

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

Add 'xy' to each side of the equation.
-1xy + 2x3 + xy + -1y2 = 0 + xy

Reorder the terms:
-1xy + xy + 2x3 + -1y2 = 0 + xy

Combine like terms: -1xy + xy = 0
0 + 2x3 + -1y2 = 0 + xy
2x3 + -1y2 = 0 + xy
Remove the zero:
2x3 + -1y2 = xy

Add '-2x3' to each side of the equation.
2x3 + -2x3 + -1y2 = xy + -2x3

Combine like terms: 2x3 + -2x3 = 0
0 + -1y2 = xy + -2x3
-1y2 = xy + -2x3

Add 'y2' to each side of the equation.
-1y2 + y2 = xy + -2x3 + y2

Combine like terms: -1y2 + y2 = 0
0 = xy + -2x3 + y2

Simplifying
0 = xy + -2x3 + y2

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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