(2xy-6x^2)dx+(x^2-y)dy=0

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Solution for (2xy-6x^2)dx+(x^2-y)dy=0 equation: 


Simplifying
(2xy + -6x2) * dx + (x2 + -1y) * dy = 0

Reorder the terms for easier multiplication:
dx(2xy + -6x2) + (x2 + -1y) * dy = 0
(2xy * dx + -6x2 * dx) + (x2 + -1y) * dy = 0
(2dx2y + -6dx3) + (x2 + -1y) * dy = 0

Reorder the terms for easier multiplication:
2dx2y + -6dx3 + dy(x2 + -1y) = 0
2dx2y + -6dx3 + (x2 * dy + -1y * dy) = 0
2dx2y + -6dx3 + (dx2y + -1dy2) = 0

Reorder the terms:
2dx2y + dx2y + -6dx3 + -1dy2 = 0

Combine like terms: 2dx2y + dx2y = 3dx2y
3dx2y + -6dx3 + -1dy2 = 0

Solving
3dx2y + -6dx3 + -1dy2 = 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(3x2y + -6x3 + -1y2) = 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 '(3x2y + -6x3 + -1y2)' equal to zero and attempt to solve:

Simplifying
3x2y + -6x3 + -1y2 = 0

Solving
3x2y + -6x3 + -1y2 = 0

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

Add '-3x2y' to each side of the equation.
3x2y + -6x3 + -3x2y + -1y2 = 0 + -3x2y

Reorder the terms:
3x2y + -3x2y + -6x3 + -1y2 = 0 + -3x2y

Combine like terms: 3x2y + -3x2y = 0
0 + -6x3 + -1y2 = 0 + -3x2y
-6x3 + -1y2 = 0 + -3x2y
Remove the zero:
-6x3 + -1y2 = -3x2y

Add '6x3' to each side of the equation.
-6x3 + 6x3 + -1y2 = -3x2y + 6x3

Combine like terms: -6x3 + 6x3 = 0
0 + -1y2 = -3x2y + 6x3
-1y2 = -3x2y + 6x3

Add 'y2' to each side of the equation.
-1y2 + y2 = -3x2y + 6x3 + y2

Combine like terms: -1y2 + y2 = 0
0 = -3x2y + 6x3 + y2

Simplifying
0 = -3x2y + 6x3 + y2

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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