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

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


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

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

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

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

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

Combine like terms: dy2 + -6dy2 = -5dy2
1dxy + -5dy2 = 0

Solving
1dxy + -5dy2 = 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), 'dy'.
dy(x + -5y) = 0


Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve:

Simplifying
dy = 0

Solving
dy = 0

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

Simplifying
dy = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(x + -5y)' equal to zero and attempt to solve:

Simplifying
x + -5y = 0

Solving
x + -5y = 0

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

Add '-1x' to each side of the equation.
x + -1x + -5y = 0 + -1x

Combine like terms: x + -1x = 0
0 + -5y = 0 + -1x
-5y = 0 + -1x
Remove the zero:
-5y = -1x

Add '5y' to each side of the equation.
-5y + 5y = -1x + 5y

Combine like terms: -5y + 5y = 0
0 = -1x + 5y

Simplifying
0 = -1x + 5y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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