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

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


Simplifying
(4x + 3y2) * dx + -3y(1 + x2) * dy = 0

Reorder the terms for easier multiplication:
dx(4x + 3y2) + -3y(1 + x2) * dy = 0
(4x * dx + 3y2 * dx) + -3y(1 + x2) * dy = 0

Reorder the terms:
(3dxy2 + 4dx2) + -3y(1 + x2) * dy = 0
(3dxy2 + 4dx2) + -3y(1 + x2) * dy = 0

Reorder the terms for easier multiplication:
3dxy2 + 4dx2 + -3y * dy(1 + x2) = 0

Multiply y * dy
3dxy2 + 4dx2 + -3dy2(1 + x2) = 0
3dxy2 + 4dx2 + (1 * -3dy2 + x2 * -3dy2) = 0

Reorder the terms:
3dxy2 + 4dx2 + (-3dx2y2 + -3dy2) = 0
3dxy2 + 4dx2 + (-3dx2y2 + -3dy2) = 0

Solving
3dxy2 + 4dx2 + -3dx2y2 + -3dy2 = 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(3xy2 + 4x2 + -3x2y2 + -3y2) = 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 '(3xy2 + 4x2 + -3x2y2 + -3y2)' equal to zero and attempt to solve:

Simplifying
3xy2 + 4x2 + -3x2y2 + -3y2 = 0

Solving
3xy2 + 4x2 + -3x2y2 + -3y2 = 0

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

Add '-3xy2' to each side of the equation.
3xy2 + 4x2 + -3x2y2 + -3xy2 + -3y2 = 0 + -3xy2

Reorder the terms:
3xy2 + -3xy2 + 4x2 + -3x2y2 + -3y2 = 0 + -3xy2

Combine like terms: 3xy2 + -3xy2 = 0
0 + 4x2 + -3x2y2 + -3y2 = 0 + -3xy2
4x2 + -3x2y2 + -3y2 = 0 + -3xy2
Remove the zero:
4x2 + -3x2y2 + -3y2 = -3xy2

Add '-4x2' to each side of the equation.
4x2 + -3x2y2 + -4x2 + -3y2 = -3xy2 + -4x2

Reorder the terms:
4x2 + -4x2 + -3x2y2 + -3y2 = -3xy2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
0 + -3x2y2 + -3y2 = -3xy2 + -4x2
-3x2y2 + -3y2 = -3xy2 + -4x2

Add '3x2y2' to each side of the equation.
-3x2y2 + 3x2y2 + -3y2 = -3xy2 + -4x2 + 3x2y2

Combine like terms: -3x2y2 + 3x2y2 = 0
0 + -3y2 = -3xy2 + -4x2 + 3x2y2
-3y2 = -3xy2 + -4x2 + 3x2y2

Add '3y2' to each side of the equation.
-3y2 + 3y2 = -3xy2 + -4x2 + 3x2y2 + 3y2

Combine like terms: -3y2 + 3y2 = 0
0 = -3xy2 + -4x2 + 3x2y2 + 3y2

Simplifying
0 = -3xy2 + -4x2 + 3x2y2 + 3y2

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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