(3x+2y^3)dx+(x+4xy+5y^2)dy=0

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Solution for (3x+2y^3)dx+(x+4xy+5y^2)dy=0 equation: 


Simplifying
(3x + 2y3) * dx + (x + 4xy + 5y2) * dy = 0

Reorder the terms for easier multiplication:
dx(3x + 2y3) + (x + 4xy + 5y2) * dy = 0
(3x * dx + 2y3 * dx) + (x + 4xy + 5y2) * dy = 0

Reorder the terms:
(2dxy3 + 3dx2) + (x + 4xy + 5y2) * dy = 0
(2dxy3 + 3dx2) + (x + 4xy + 5y2) * dy = 0

Reorder the terms for easier multiplication:
2dxy3 + 3dx2 + dy(x + 4xy + 5y2) = 0
2dxy3 + 3dx2 + (x * dy + 4xy * dy + 5y2 * dy) = 0
2dxy3 + 3dx2 + (dxy + 4dxy2 + 5dy3) = 0

Reorder the terms:
dxy + 4dxy2 + 2dxy3 + 3dx2 + 5dy3 = 0

Solving
dxy + 4dxy2 + 2dxy3 + 3dx2 + 5dy3 = 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(xy + 4xy2 + 2xy3 + 3x2 + 5y3) = 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 '(xy + 4xy2 + 2xy3 + 3x2 + 5y3)' equal to zero and attempt to solve:

Simplifying
xy + 4xy2 + 2xy3 + 3x2 + 5y3 = 0

Solving
xy + 4xy2 + 2xy3 + 3x2 + 5y3 = 0

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

Add '-1xy' to each side of the equation.
xy + 4xy2 + 2xy3 + 3x2 + -1xy + 5y3 = 0 + -1xy

Reorder the terms:
xy + -1xy + 4xy2 + 2xy3 + 3x2 + 5y3 = 0 + -1xy

Combine like terms: xy + -1xy = 0
0 + 4xy2 + 2xy3 + 3x2 + 5y3 = 0 + -1xy
4xy2 + 2xy3 + 3x2 + 5y3 = 0 + -1xy
Remove the zero:
4xy2 + 2xy3 + 3x2 + 5y3 = -1xy

Add '-4xy2' to each side of the equation.
4xy2 + 2xy3 + 3x2 + -4xy2 + 5y3 = -1xy + -4xy2

Reorder the terms:
4xy2 + -4xy2 + 2xy3 + 3x2 + 5y3 = -1xy + -4xy2

Combine like terms: 4xy2 + -4xy2 = 0
0 + 2xy3 + 3x2 + 5y3 = -1xy + -4xy2
2xy3 + 3x2 + 5y3 = -1xy + -4xy2

Add '-2xy3' to each side of the equation.
2xy3 + 3x2 + -2xy3 + 5y3 = -1xy + -4xy2 + -2xy3

Reorder the terms:
2xy3 + -2xy3 + 3x2 + 5y3 = -1xy + -4xy2 + -2xy3

Combine like terms: 2xy3 + -2xy3 = 0
0 + 3x2 + 5y3 = -1xy + -4xy2 + -2xy3
3x2 + 5y3 = -1xy + -4xy2 + -2xy3

Add '-3x2' to each side of the equation.
3x2 + -3x2 + 5y3 = -1xy + -4xy2 + -2xy3 + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + 5y3 = -1xy + -4xy2 + -2xy3 + -3x2
5y3 = -1xy + -4xy2 + -2xy3 + -3x2

Add '-5y3' to each side of the equation.
5y3 + -5y3 = -1xy + -4xy2 + -2xy3 + -3x2 + -5y3

Combine like terms: 5y3 + -5y3 = 0
0 = -1xy + -4xy2 + -2xy3 + -3x2 + -5y3

Simplifying
0 = -1xy + -4xy2 + -2xy3 + -3x2 + -5y3

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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