(X+y+1)dx-dy=0

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Solution for (X+y+1)dx-dy=0 equation: 


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

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

Reorder the terms for easier multiplication:
dx(1 + X + y) + -1dy = 0
(1 * dx + X * dx + y * dx) + -1dy = 0
(1dx + dxX + dxy) + -1dy = 0

Solving
1dx + dxX + dxy + -1dy = 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(x + xX + xy + -1y) = 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 '(x + xX + xy + -1y)' equal to zero and attempt to solve:

Simplifying
x + xX + xy + -1y = 0

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

Reorder the terms:
x + -1x + xX + xy + -1y = 0 + -1x

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

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

Reorder the terms:
xX + -1xX + xy + -1y = -1x + -1xX

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

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

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

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

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

Simplifying
0 = -1x + -1xX + -1xy + y

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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