(x+y-1)dx+(ey+x)dy=

Solution for (x+y-1)dx+(ey+x)dy= equation:

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

Reorder the terms:
(-1 + x + y) * dx + (ey + x) * dy = 0

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

Reorder the terms:
(-1dx + dxy + dx2) + (ey + x) * dy = 0
(-1dx + dxy + dx2) + (ey + x) * dy = 0

Reorder the terms for easier multiplication:
-1dx + dxy + dx2 + dy(ey + x) = 0
-1dx + dxy + dx2 + (ey * dy + x * dy) = 0
-1dx + dxy + dx2 + (dey2 + dxy) = 0

Reorder the terms:
dey2 + -1dx + dxy + dxy + dx2 = 0

Combine like terms: dxy + dxy = 2dxy
dey2 + -1dx + 2dxy + dx2 = 0

Solving
dey2 + -1dx + 2dxy + dx2 = 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(ey2 + -1x + 2xy + x2) = 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 '(ey2 + -1x + 2xy + x2)' equal to zero and attempt to solve:

Simplifying
ey2 + -1x + 2xy + x2 = 0

Solving
ey2 + -1x + 2xy + x2 = 0

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

Add '-1ey2' to each side of the equation.
ey2 + -1x + 2xy + -1ey2 + x2 = 0 + -1ey2

Reorder the terms:
ey2 + -1ey2 + -1x + 2xy + x2 = 0 + -1ey2

Combine like terms: ey2 + -1ey2 = 0
0 + -1x + 2xy + x2 = 0 + -1ey2
-1x + 2xy + x2 = 0 + -1ey2
Remove the zero:
-1x + 2xy + x2 = -1ey2

Add 'x' to each side of the equation.
-1x + 2xy + x + x2 = -1ey2 + x

Reorder the terms:
-1x + x + 2xy + x2 = -1ey2 + x

Combine like terms: -1x + x = 0
0 + 2xy + x2 = -1ey2 + x
2xy + x2 = -1ey2 + x

Add '-2xy' to each side of the equation.
2xy + -2xy + x2 = -1ey2 + x + -2xy

Combine like terms: 2xy + -2xy = 0
0 + x2 = -1ey2 + x + -2xy
x2 = -1ey2 + x + -2xy

Add '-1x2' to each side of the equation.
x2 + -1x2 = -1ey2 + x + -2xy + -1x2

Combine like terms: x2 + -1x2 = 0
0 = -1ey2 + x + -2xy + -1x2

Simplifying
0 = -1ey2 + x + -2xy + -1x2

The solution to this equation could not be determined.

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