(4xy^3+3y^2+1)dx+(6x^2y^2+6xy)dy=0

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Solution for (4xy^3+3y^2+1)dx+(6x^2y^2+6xy)dy=0 equation: 


Simplifying
(4xy3 + 3y2 + 1) * dx + (6x2y2 + 6xy) * dy = 0

Reorder the terms:
(1 + 4xy3 + 3y2) * dx + (6x2y2 + 6xy) * dy = 0

Reorder the terms for easier multiplication:
dx(1 + 4xy3 + 3y2) + (6x2y2 + 6xy) * dy = 0
(1 * dx + 4xy3 * dx + 3y2 * dx) + (6x2y2 + 6xy) * dy = 0

Reorder the terms:
(1dx + 3dxy2 + 4dx2y3) + (6x2y2 + 6xy) * dy = 0
(1dx + 3dxy2 + 4dx2y3) + (6x2y2 + 6xy) * dy = 0

Reorder the terms:
1dx + 3dxy2 + 4dx2y3 + (6xy + 6x2y2) * dy = 0

Reorder the terms for easier multiplication:
1dx + 3dxy2 + 4dx2y3 + dy(6xy + 6x2y2) = 0
1dx + 3dxy2 + 4dx2y3 + (6xy * dy + 6x2y2 * dy) = 0
1dx + 3dxy2 + 4dx2y3 + (6dxy2 + 6dx2y3) = 0

Reorder the terms:
1dx + 3dxy2 + 6dxy2 + 4dx2y3 + 6dx2y3 = 0

Combine like terms: 3dxy2 + 6dxy2 = 9dxy2
1dx + 9dxy2 + 4dx2y3 + 6dx2y3 = 0

Combine like terms: 4dx2y3 + 6dx2y3 = 10dx2y3
1dx + 9dxy2 + 10dx2y3 = 0

Solving
1dx + 9dxy2 + 10dx2y3 = 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), 'dx'.
dx(1 + 9y2 + 10xy3) = 0


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

Simplifying
dx = 0

Solving
dx = 0

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

Simplifying
dx = 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 '(1 + 9y2 + 10xy3)' equal to zero and attempt to solve:

Simplifying
1 + 9y2 + 10xy3 = 0

Reorder the terms:
1 + 10xy3 + 9y2 = 0

Solving
1 + 10xy3 + 9y2 = 0

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

Add '-1' to each side of the equation.
1 + 10xy3 + -1 + 9y2 = 0 + -1

Reorder the terms:
1 + -1 + 10xy3 + 9y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 10xy3 + 9y2 = 0 + -1
10xy3 + 9y2 = 0 + -1

Combine like terms: 0 + -1 = -1
10xy3 + 9y2 = -1

Add '-10xy3' to each side of the equation.
10xy3 + -10xy3 + 9y2 = -1 + -10xy3

Combine like terms: 10xy3 + -10xy3 = 0
0 + 9y2 = -1 + -10xy3
9y2 = -1 + -10xy3

Add '-9y2' to each side of the equation.
9y2 + -9y2 = -1 + -10xy3 + -9y2

Combine like terms: 9y2 + -9y2 = 0
0 = -1 + -10xy3 + -9y2

Simplifying
0 = -1 + -10xy3 + -9y2

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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