(6x+y^2)dx+y(2x-3y)dy=0

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Solution for (6x+y^2)dx+y(2x-3y)dy=0 equation: 


Simplifying
(6x + y2) * dx + y(2x + -3y) * dy = 0

Reorder the terms for easier multiplication:
dx(6x + y2) + y(2x + -3y) * dy = 0
(6x * dx + y2 * dx) + y(2x + -3y) * dy = 0

Reorder the terms:
(dxy2 + 6dx2) + y(2x + -3y) * dy = 0
(dxy2 + 6dx2) + y(2x + -3y) * dy = 0

Reorder the terms for easier multiplication:
dxy2 + 6dx2 + y * dy(2x + -3y) = 0

Multiply y * dy
dxy2 + 6dx2 + dy2(2x + -3y) = 0
dxy2 + 6dx2 + (2x * dy2 + -3y * dy2) = 0
dxy2 + 6dx2 + (2dxy2 + -3dy3) = 0

Reorder the terms:
dxy2 + 2dxy2 + 6dx2 + -3dy3 = 0

Combine like terms: dxy2 + 2dxy2 = 3dxy2
3dxy2 + 6dx2 + -3dy3 = 0

Solving
3dxy2 + 6dx2 + -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), '3d'.
3d(xy2 + 2x2 + -1y3) = 0

Ignore the factor 3.

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 '(xy2 + 2x2 + -1y3)' equal to zero and attempt to solve:

Simplifying
xy2 + 2x2 + -1y3 = 0

Solving
xy2 + 2x2 + -1y3 = 0

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

Add '-1xy2' to each side of the equation.
xy2 + 2x2 + -1xy2 + -1y3 = 0 + -1xy2

Reorder the terms:
xy2 + -1xy2 + 2x2 + -1y3 = 0 + -1xy2

Combine like terms: xy2 + -1xy2 = 0
0 + 2x2 + -1y3 = 0 + -1xy2
2x2 + -1y3 = 0 + -1xy2
Remove the zero:
2x2 + -1y3 = -1xy2

Add '-2x2' to each side of the equation.
2x2 + -2x2 + -1y3 = -1xy2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + -1y3 = -1xy2 + -2x2
-1y3 = -1xy2 + -2x2

Add 'y3' to each side of the equation.
-1y3 + y3 = -1xy2 + -2x2 + y3

Combine like terms: -1y3 + y3 = 0
0 = -1xy2 + -2x2 + y3

Simplifying
0 = -1xy2 + -2x2 + y3

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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