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

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


Simplifying
(x + -3xy) * dx + (2y + x3) * dy = 0

Reorder the terms for easier multiplication:
dx(x + -3xy) + (2y + x3) * dy = 0
(x * dx + -3xy * dx) + (2y + x3) * dy = 0
(dx2 + -3dx2y) + (2y + x3) * dy = 0

Reorder the terms:
dx2 + -3dx2y + (x3 + 2y) * dy = 0

Reorder the terms for easier multiplication:
dx2 + -3dx2y + dy(x3 + 2y) = 0
dx2 + -3dx2y + (x3 * dy + 2y * dy) = 0
dx2 + -3dx2y + (dx3y + 2dy2) = 0

Solving
dx2 + -3dx2y + dx3y + 2dy2 = 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(x2 + -3x2y + x3y + 2y2) = 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 '(x2 + -3x2y + x3y + 2y2)' equal to zero and attempt to solve:

Simplifying
x2 + -3x2y + x3y + 2y2 = 0

Solving
x2 + -3x2y + x3y + 2y2 = 0

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

Add '-1x2' to each side of the equation.
x2 + -3x2y + x3y + -1x2 + 2y2 = 0 + -1x2

Reorder the terms:
x2 + -1x2 + -3x2y + x3y + 2y2 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
0 + -3x2y + x3y + 2y2 = 0 + -1x2
-3x2y + x3y + 2y2 = 0 + -1x2
Remove the zero:
-3x2y + x3y + 2y2 = -1x2

Add '3x2y' to each side of the equation.
-3x2y + x3y + 3x2y + 2y2 = -1x2 + 3x2y

Reorder the terms:
-3x2y + 3x2y + x3y + 2y2 = -1x2 + 3x2y

Combine like terms: -3x2y + 3x2y = 0
0 + x3y + 2y2 = -1x2 + 3x2y
x3y + 2y2 = -1x2 + 3x2y

Add '-1x3y' to each side of the equation.
x3y + -1x3y + 2y2 = -1x2 + 3x2y + -1x3y

Combine like terms: x3y + -1x3y = 0
0 + 2y2 = -1x2 + 3x2y + -1x3y
2y2 = -1x2 + 3x2y + -1x3y

Add '-2y2' to each side of the equation.
2y2 + -2y2 = -1x2 + 3x2y + -1x3y + -2y2

Combine like terms: 2y2 + -2y2 = 0
0 = -1x2 + 3x2y + -1x3y + -2y2

Simplifying
0 = -1x2 + 3x2y + -1x3y + -2y2

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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