2y(y^2-x)dy=dx

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


Simplifying
2y(y2 + -1x) * dy = dx

Reorder the terms:
2y(-1x + y2) * dy = dx

Reorder the terms for easier multiplication:
2y * dy(-1x + y2) = dx

Multiply y * dy
2dy2(-1x + y2) = dx
(-1x * 2dy2 + y2 * 2dy2) = dx
(-2dxy2 + 2dy4) = dx

Solving
-2dxy2 + 2dy4 = dx

Solving for variable 'd'.

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

Add '-1dx' to each side of the equation.
-2dxy2 + -1dx + 2dy4 = dx + -1dx

Reorder the terms:
-1dx + -2dxy2 + 2dy4 = dx + -1dx

Combine like terms: dx + -1dx = 0
-1dx + -2dxy2 + 2dy4 = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(-1x + -2xy2 + 2y4) = 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 + -2xy2 + 2y4)' equal to zero and attempt to solve:

Simplifying
-1x + -2xy2 + 2y4 = 0

Solving
-1x + -2xy2 + 2y4 = 0

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

Add 'x' to each side of the equation.
-1x + -2xy2 + x + 2y4 = 0 + x

Reorder the terms:
-1x + x + -2xy2 + 2y4 = 0 + x

Combine like terms: -1x + x = 0
0 + -2xy2 + 2y4 = 0 + x
-2xy2 + 2y4 = 0 + x
Remove the zero:
-2xy2 + 2y4 = x

Add '2xy2' to each side of the equation.
-2xy2 + 2xy2 + 2y4 = x + 2xy2

Combine like terms: -2xy2 + 2xy2 = 0
0 + 2y4 = x + 2xy2
2y4 = x + 2xy2

Add '-2y4' to each side of the equation.
2y4 + -2y4 = x + 2xy2 + -2y4

Combine like terms: 2y4 + -2y4 = 0
0 = x + 2xy2 + -2y4

Simplifying
0 = x + 2xy2 + -2y4

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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