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

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


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

Reorder the terms for easier multiplication:
dy(x + 3y2) + (6x + y) * dx = 0
(x * dy + 3y2 * dy) + (6x + y) * dx = 0
(dxy + 3dy3) + (6x + y) * dx = 0

Reorder the terms for easier multiplication:
dxy + 3dy3 + dx(6x + y) = 0
dxy + 3dy3 + (6x * dx + y * dx) = 0

Reorder the terms:
dxy + 3dy3 + (dxy + 6dx2) = 0
dxy + 3dy3 + (dxy + 6dx2) = 0

Reorder the terms:
dxy + dxy + 6dx2 + 3dy3 = 0

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

Solving
2dxy + 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), 'd'.
d(2xy + 6x2 + 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 '(2xy + 6x2 + 3y3)' equal to zero and attempt to solve:

Simplifying
2xy + 6x2 + 3y3 = 0

Solving
2xy + 6x2 + 3y3 = 0

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

Add '-2xy' to each side of the equation.
2xy + 6x2 + -2xy + 3y3 = 0 + -2xy

Reorder the terms:
2xy + -2xy + 6x2 + 3y3 = 0 + -2xy

Combine like terms: 2xy + -2xy = 0
0 + 6x2 + 3y3 = 0 + -2xy
6x2 + 3y3 = 0 + -2xy
Remove the zero:
6x2 + 3y3 = -2xy

Add '-6x2' to each side of the equation.
6x2 + -6x2 + 3y3 = -2xy + -6x2

Combine like terms: 6x2 + -6x2 = 0
0 + 3y3 = -2xy + -6x2
3y3 = -2xy + -6x2

Add '-3y3' to each side of the equation.
3y3 + -3y3 = -2xy + -6x2 + -3y3

Combine like terms: 3y3 + -3y3 = 0
0 = -2xy + -6x2 + -3y3

Simplifying
0 = -2xy + -6x2 + -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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