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

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


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

Reorder the terms:
(-2 + x) * dx + (2x + y) * dy = 0

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

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

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

Solving
-2dx + 2dxy + dx2 + dy2 = 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(-2x + 2xy + x2 + y2) = 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 '(-2x + 2xy + x2 + y2)' equal to zero and attempt to solve:

Simplifying
-2x + 2xy + x2 + y2 = 0

Solving
-2x + 2xy + x2 + y2 = 0

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

Add '2x' to each side of the equation.
-2x + 2xy + x2 + 2x + y2 = 0 + 2x

Reorder the terms:
-2x + 2x + 2xy + x2 + y2 = 0 + 2x

Combine like terms: -2x + 2x = 0
0 + 2xy + x2 + y2 = 0 + 2x
2xy + x2 + y2 = 0 + 2x
Remove the zero:
2xy + x2 + y2 = 2x

Add '-2xy' to each side of the equation.
2xy + x2 + -2xy + y2 = 2x + -2xy

Reorder the terms:
2xy + -2xy + x2 + y2 = 2x + -2xy

Combine like terms: 2xy + -2xy = 0
0 + x2 + y2 = 2x + -2xy
x2 + y2 = 2x + -2xy

Add '-1x2' to each side of the equation.
x2 + -1x2 + y2 = 2x + -2xy + -1x2

Combine like terms: x2 + -1x2 = 0
0 + y2 = 2x + -2xy + -1x2
y2 = 2x + -2xy + -1x2

Add '-1y2' to each side of the equation.
y2 + -1y2 = 2x + -2xy + -1x2 + -1y2

Combine like terms: y2 + -1y2 = 0
0 = 2x + -2xy + -1x2 + -1y2

Simplifying
0 = 2x + -2xy + -1x2 + -1y2

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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