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

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


Simplifying
(2x + 3x2y) * dx + -1(x3 + -3y2) * dy = 0

Reorder the terms for easier multiplication:
dx(2x + 3x2y) + -1(x3 + -3y2) * dy = 0
(2x * dx + 3x2y * dx) + -1(x3 + -3y2) * dy = 0
(2dx2 + 3dx3y) + -1(x3 + -3y2) * dy = 0

Reorder the terms for easier multiplication:
2dx2 + 3dx3y + -1dy(x3 + -3y2) = 0
2dx2 + 3dx3y + (x3 * -1dy + -3y2 * -1dy) = 0
2dx2 + 3dx3y + (-1dx3y + 3dy3) = 0

Combine like terms: 3dx3y + -1dx3y = 2dx3y
2dx2 + 2dx3y + 3dy3 = 0

Solving
2dx2 + 2dx3y + 3dy3 = 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(2x2 + 2x3y + 3y3) = 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 '(2x2 + 2x3y + 3y3)' equal to zero and attempt to solve:

Simplifying
2x2 + 2x3y + 3y3 = 0

Solving
2x2 + 2x3y + 3y3 = 0

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

Add '-2x2' to each side of the equation.
2x2 + 2x3y + -2x2 + 3y3 = 0 + -2x2

Reorder the terms:
2x2 + -2x2 + 2x3y + 3y3 = 0 + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + 2x3y + 3y3 = 0 + -2x2
2x3y + 3y3 = 0 + -2x2
Remove the zero:
2x3y + 3y3 = -2x2

Add '-2x3y' to each side of the equation.
2x3y + -2x3y + 3y3 = -2x2 + -2x3y

Combine like terms: 2x3y + -2x3y = 0
0 + 3y3 = -2x2 + -2x3y
3y3 = -2x2 + -2x3y

Add '-3y3' to each side of the equation.
3y3 + -3y3 = -2x2 + -2x3y + -3y3

Combine like terms: 3y3 + -3y3 = 0
0 = -2x2 + -2x3y + -3y3

Simplifying
0 = -2x2 + -2x3y + -3y3

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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