(y^2)dy+(2xy^3-6x)dx=0

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Solution for (y^2)dy+(2xy^3-6x)dx=0 equation: 


Simplifying
(y2) * dy + (2xy3 + -6x) * dx = 0

Multiply y2 * dy
dy3 + (2xy3 + -6x) * dx = 0

Reorder the terms:
dy3 + (-6x + 2xy3) * dx = 0

Reorder the terms for easier multiplication:
dy3 + dx(-6x + 2xy3) = 0
dy3 + (-6x * dx + 2xy3 * dx) = 0
dy3 + (-6dx2 + 2dx2y3) = 0

Reorder the terms:
-6dx2 + 2dx2y3 + dy3 = 0

Solving
-6dx2 + 2dx2y3 + dy3 = 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(-6x2 + 2x2y3 + y3) = 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 '(-6x2 + 2x2y3 + y3)' equal to zero and attempt to solve:

Simplifying
-6x2 + 2x2y3 + y3 = 0

Solving
-6x2 + 2x2y3 + y3 = 0

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

Add '6x2' to each side of the equation.
-6x2 + 2x2y3 + 6x2 + y3 = 0 + 6x2

Reorder the terms:
-6x2 + 6x2 + 2x2y3 + y3 = 0 + 6x2

Combine like terms: -6x2 + 6x2 = 0
0 + 2x2y3 + y3 = 0 + 6x2
2x2y3 + y3 = 0 + 6x2
Remove the zero:
2x2y3 + y3 = 6x2

Add '-2x2y3' to each side of the equation.
2x2y3 + -2x2y3 + y3 = 6x2 + -2x2y3

Combine like terms: 2x2y3 + -2x2y3 = 0
0 + y3 = 6x2 + -2x2y3
y3 = 6x2 + -2x2y3

Add '-1y3' to each side of the equation.
y3 + -1y3 = 6x2 + -2x2y3 + -1y3

Combine like terms: y3 + -1y3 = 0
0 = 6x2 + -2x2y3 + -1y3

Simplifying
0 = 6x2 + -2x2y3 + -1y3

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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