(2y)dx+(2x-4y)dy=0

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Solution for (2y)dx+(2x-4y)dy=0 equation: 


Simplifying
(2y) * dx + (2x + -4y) * dy = 0

Remove parenthesis around (2y)
2y * dx + (2x + -4y) * dy = 0

Multiply y * dx
2dxy + (2x + -4y) * dy = 0

Reorder the terms for easier multiplication:
2dxy + dy(2x + -4y) = 0
2dxy + (2x * dy + -4y * dy) = 0
2dxy + (2dxy + -4dy2) = 0

Combine like terms: 2dxy + 2dxy = 4dxy
4dxy + -4dy2 = 0

Solving
4dxy + -4dy2 = 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), '4dy'.
4dy(x + -1y) = 0

Ignore the factor 4.

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 + -1y)' equal to zero and attempt to solve:

Simplifying
x + -1y = 0

Solving
x + -1y = 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 + -1y = 0 + -1x

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

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

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

Simplifying
0 = -1x + y

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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