(3yx^2-y^3)dx-(3xy^2-X^3)dy=0

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Solution for (3yx^2-y^3)dx-(3xy^2-X^3)dy=0 equation: 


Simplifying
(3yx2 + -1y3) * dx + -1(3xy2 + -1X3) * dy = 0

Reorder the terms for easier multiplication:
dx(3x2y + -1y3) + -1(3xy2 + -1X3) * dy = 0
(3x2y * dx + -1y3 * dx) + -1(3xy2 + -1X3) * dy = 0

Reorder the terms:
(-1dxy3 + 3dx3y) + -1(3xy2 + -1X3) * dy = 0
(-1dxy3 + 3dx3y) + -1(3xy2 + -1X3) * dy = 0

Reorder the terms:
-1dxy3 + 3dx3y + -1(-1X3 + 3xy2) * dy = 0

Reorder the terms for easier multiplication:
-1dxy3 + 3dx3y + -1dy(-1X3 + 3xy2) = 0
-1dxy3 + 3dx3y + (-1X3 * -1dy + 3xy2 * -1dy) = 0

Reorder the terms:
-1dxy3 + 3dx3y + (-3dxy3 + 1dyX3) = 0
-1dxy3 + 3dx3y + (-3dxy3 + 1dyX3) = 0

Reorder the terms:
-1dxy3 + -3dxy3 + 3dx3y + 1dyX3 = 0

Combine like terms: -1dxy3 + -3dxy3 = -4dxy3
-4dxy3 + 3dx3y + 1dyX3 = 0

Solving
-4dxy3 + 3dx3y + 1dyX3 = 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(-4xy2 + 3x3 + X3) = 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 '(-4xy2 + 3x3 + X3)' equal to zero and attempt to solve:

Simplifying
-4xy2 + 3x3 + X3 = 0

Reorder the terms:
X3 + -4xy2 + 3x3 = 0

Solving
X3 + -4xy2 + 3x3 = 0

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

Add '-1X3' to each side of the equation.
X3 + -4xy2 + -1X3 + 3x3 = 0 + -1X3

Reorder the terms:
X3 + -1X3 + -4xy2 + 3x3 = 0 + -1X3

Combine like terms: X3 + -1X3 = 0
0 + -4xy2 + 3x3 = 0 + -1X3
-4xy2 + 3x3 = 0 + -1X3
Remove the zero:
-4xy2 + 3x3 = -1X3

Add '4xy2' to each side of the equation.
-4xy2 + 4xy2 + 3x3 = -1X3 + 4xy2

Combine like terms: -4xy2 + 4xy2 = 0
0 + 3x3 = -1X3 + 4xy2
3x3 = -1X3 + 4xy2

Add '-3x3' to each side of the equation.
3x3 + -3x3 = -1X3 + 4xy2 + -3x3

Combine like terms: 3x3 + -3x3 = 0
0 = -1X3 + 4xy2 + -3x3

Simplifying
0 = -1X3 + 4xy2 + -3x3

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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