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

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


Simplifying
(4x3y3 + 3x2) * dx + (3x4 + y2 + 6y2) * dy = 0

Reorder the terms:
(3x2 + 4x3y3) * dx + (3x4 + y2 + 6y2) * dy = 0

Reorder the terms for easier multiplication:
dx(3x2 + 4x3y3) + (3x4 + y2 + 6y2) * dy = 0
(3x2 * dx + 4x3y3 * dx) + (3x4 + y2 + 6y2) * dy = 0
(3dx3 + 4dx4y3) + (3x4 + y2 + 6y2) * dy = 0

Combine like terms: y2 + 6y2 = 7y2
3dx3 + 4dx4y3 + (3x4 + 7y2) * dy = 0

Reorder the terms for easier multiplication:
3dx3 + 4dx4y3 + dy(3x4 + 7y2) = 0
3dx3 + 4dx4y3 + (3x4 * dy + 7y2 * dy) = 0
3dx3 + 4dx4y3 + (3dx4y + 7dy3) = 0

Reorder the terms:
3dx3 + 3dx4y + 4dx4y3 + 7dy3 = 0

Solving
3dx3 + 3dx4y + 4dx4y3 + 7dy3 = 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(3x3 + 3x4y + 4x4y3 + 7y3) = 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 '(3x3 + 3x4y + 4x4y3 + 7y3)' equal to zero and attempt to solve:

Simplifying
3x3 + 3x4y + 4x4y3 + 7y3 = 0

Solving
3x3 + 3x4y + 4x4y3 + 7y3 = 0

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

Add '-3x3' to each side of the equation.
3x3 + 3x4y + 4x4y3 + -3x3 + 7y3 = 0 + -3x3

Reorder the terms:
3x3 + -3x3 + 3x4y + 4x4y3 + 7y3 = 0 + -3x3

Combine like terms: 3x3 + -3x3 = 0
0 + 3x4y + 4x4y3 + 7y3 = 0 + -3x3
3x4y + 4x4y3 + 7y3 = 0 + -3x3
Remove the zero:
3x4y + 4x4y3 + 7y3 = -3x3

Add '-3x4y' to each side of the equation.
3x4y + 4x4y3 + -3x4y + 7y3 = -3x3 + -3x4y

Reorder the terms:
3x4y + -3x4y + 4x4y3 + 7y3 = -3x3 + -3x4y

Combine like terms: 3x4y + -3x4y = 0
0 + 4x4y3 + 7y3 = -3x3 + -3x4y
4x4y3 + 7y3 = -3x3 + -3x4y

Add '-4x4y3' to each side of the equation.
4x4y3 + -4x4y3 + 7y3 = -3x3 + -3x4y + -4x4y3

Combine like terms: 4x4y3 + -4x4y3 = 0
0 + 7y3 = -3x3 + -3x4y + -4x4y3
7y3 = -3x3 + -3x4y + -4x4y3

Add '-7y3' to each side of the equation.
7y3 + -7y3 = -3x3 + -3x4y + -4x4y3 + -7y3

Combine like terms: 7y3 + -7y3 = 0
0 = -3x3 + -3x4y + -4x4y3 + -7y3

Simplifying
0 = -3x3 + -3x4y + -4x4y3 + -7y3

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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