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

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


Simplifying
6y2dx + -1(2x3 + y) * dy = 0

Reorder the terms for easier multiplication:
6dxy2 + -1dy(2x3 + y) = 0
6dxy2 + (2x3 * -1dy + y * -1dy) = 0
6dxy2 + (-2dx3y + -1dy2) = 0

Solving
6dxy2 + -2dx3y + -1dy2 = 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), 'dy'.
dy(6xy + -2x3 + -1y) = 0


Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve:

Simplifying
dy = 0

Solving
dy = 0

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

Simplifying
dy = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(6xy + -2x3 + -1y)' equal to zero and attempt to solve:

Simplifying
6xy + -2x3 + -1y = 0

Solving
6xy + -2x3 + -1y = 0

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

Add '-6xy' to each side of the equation.
6xy + -2x3 + -6xy + -1y = 0 + -6xy

Reorder the terms:
6xy + -6xy + -2x3 + -1y = 0 + -6xy

Combine like terms: 6xy + -6xy = 0
0 + -2x3 + -1y = 0 + -6xy
-2x3 + -1y = 0 + -6xy
Remove the zero:
-2x3 + -1y = -6xy

Add '2x3' to each side of the equation.
-2x3 + 2x3 + -1y = -6xy + 2x3

Combine like terms: -2x3 + 2x3 = 0
0 + -1y = -6xy + 2x3
-1y = -6xy + 2x3

Add 'y' to each side of the equation.
-1y + y = -6xy + 2x3 + y

Combine like terms: -1y + y = 0
0 = -6xy + 2x3 + y

Simplifying
0 = -6xy + 2x3 + y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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