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

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


Simplifying
(3x2 * y + y2) * dx + (3x3 + -1y2 + 4xy) * dy = 0

Multiply x2 * y
(3x2y + y2) * dx + (3x3 + -1y2 + 4xy) * dy = 0

Reorder the terms for easier multiplication:
dx(3x2y + y2) + (3x3 + -1y2 + 4xy) * dy = 0
(3x2y * dx + y2 * dx) + (3x3 + -1y2 + 4xy) * dy = 0

Reorder the terms:
(dxy2 + 3dx3y) + (3x3 + -1y2 + 4xy) * dy = 0
(dxy2 + 3dx3y) + (3x3 + -1y2 + 4xy) * dy = 0

Reorder the terms:
dxy2 + 3dx3y + (4xy + 3x3 + -1y2) * dy = 0

Reorder the terms for easier multiplication:
dxy2 + 3dx3y + dy(4xy + 3x3 + -1y2) = 0
dxy2 + 3dx3y + (4xy * dy + 3x3 * dy + -1y2 * dy) = 0
dxy2 + 3dx3y + (4dxy2 + 3dx3y + -1dy3) = 0

Reorder the terms:
dxy2 + 4dxy2 + 3dx3y + 3dx3y + -1dy3 = 0

Combine like terms: dxy2 + 4dxy2 = 5dxy2
5dxy2 + 3dx3y + 3dx3y + -1dy3 = 0

Combine like terms: 3dx3y + 3dx3y = 6dx3y
5dxy2 + 6dx3y + -1dy3 = 0

Solving
5dxy2 + 6dx3y + -1dy3 = 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(5xy + 6x3 + -1y2) = 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 '(5xy + 6x3 + -1y2)' equal to zero and attempt to solve:

Simplifying
5xy + 6x3 + -1y2 = 0

Solving
5xy + 6x3 + -1y2 = 0

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

Add '-5xy' to each side of the equation.
5xy + 6x3 + -5xy + -1y2 = 0 + -5xy

Reorder the terms:
5xy + -5xy + 6x3 + -1y2 = 0 + -5xy

Combine like terms: 5xy + -5xy = 0
0 + 6x3 + -1y2 = 0 + -5xy
6x3 + -1y2 = 0 + -5xy
Remove the zero:
6x3 + -1y2 = -5xy

Add '-6x3' to each side of the equation.
6x3 + -6x3 + -1y2 = -5xy + -6x3

Combine like terms: 6x3 + -6x3 = 0
0 + -1y2 = -5xy + -6x3
-1y2 = -5xy + -6x3

Add 'y2' to each side of the equation.
-1y2 + y2 = -5xy + -6x3 + y2

Combine like terms: -1y2 + y2 = 0
0 = -5xy + -6x3 + y2

Simplifying
0 = -5xy + -6x3 + y2

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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