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

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


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

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

Reorder the terms:
(dxy + 2dx2) + -1(x + 6y) * dy = 0
(dxy + 2dx2) + -1(x + 6y) * dy = 0

Reorder the terms for easier multiplication:
dxy + 2dx2 + -1dy(x + 6y) = 0
dxy + 2dx2 + (x * -1dy + 6y * -1dy) = 0
dxy + 2dx2 + (-1dxy + -6dy2) = 0

Reorder the terms:
dxy + -1dxy + 2dx2 + -6dy2 = 0

Combine like terms: dxy + -1dxy = 0
0 + 2dx2 + -6dy2 = 0
2dx2 + -6dy2 = 0

Solving
2dx2 + -6dy2 = 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), '2d'.
2d(x2 + -3y2) = 0

Ignore the factor 2.

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 + -3y2)' equal to zero and attempt to solve:

Simplifying
x2 + -3y2 = 0

Solving
x2 + -3y2 = 0

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

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

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

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

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

Simplifying
0 = -1x2 + 3y2

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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