(2+2y)dx-(5-x)dy=0

Solution for (2+2y)dx-(5-x)dy=0 equation:

Simplifying
(2 + 2y) * dx + -1(5 + -1x) * dy = 0

Reorder the terms for easier multiplication:
dx(2 + 2y) + -1(5 + -1x) * dy = 0
(2 * dx + 2y * dx) + -1(5 + -1x) * dy = 0
(2dx + 2dxy) + -1(5 + -1x) * dy = 0

Reorder the terms for easier multiplication:
2dx + 2dxy + -1dy(5 + -1x) = 0
2dx + 2dxy + (5 * -1dy + -1x * -1dy) = 0

Reorder the terms:
2dx + 2dxy + (1dxy + -5dy) = 0
2dx + 2dxy + (1dxy + -5dy) = 0

Combine like terms: 2dxy + 1dxy = 3dxy
2dx + 3dxy + -5dy = 0

Solving
2dx + 3dxy + -5dy = 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 + 3xy + -5y) = 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 + 3xy + -5y)' equal to zero and attempt to solve:

Simplifying
2x + 3xy + -5y = 0

Solving
2x + 3xy + -5y = 0

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

Add '-2x' to each side of the equation.
2x + 3xy + -2x + -5y = 0 + -2x

Reorder the terms:
2x + -2x + 3xy + -5y = 0 + -2x

Combine like terms: 2x + -2x = 0
0 + 3xy + -5y = 0 + -2x
3xy + -5y = 0 + -2x
Remove the zero:
3xy + -5y = -2x

Add '-3xy' to each side of the equation.
3xy + -3xy + -5y = -2x + -3xy

Combine like terms: 3xy + -3xy = 0
0 + -5y = -2x + -3xy
-5y = -2x + -3xy

Add '5y' to each side of the equation.
-5y + 5y = -2x + -3xy + 5y

Combine like terms: -5y + 5y = 0
0 = -2x + -3xy + 5y

Simplifying
0 = -2x + -3xy + 5y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}