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

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


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

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

Multiply elosv * dx
delosvx(x + -1y) + (x + y) * dy = 0
(x * delosvx + -1y * delosvx) + (x + y) * dy = 0

Reorder the terms:
(-1delosvxy + delosvx2) + (x + y) * dy = 0
(-1delosvxy + delosvx2) + (x + y) * dy = 0

Reorder the terms for easier multiplication:
-1delosvxy + delosvx2 + dy(x + y) = 0
-1delosvxy + delosvx2 + (x * dy + y * dy) = 0
-1delosvxy + delosvx2 + (dxy + dy2) = 0

Solving
-1delosvxy + delosvx2 + dxy + 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(-1elosvxy + elosvx2 + xy + 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 '(-1elosvxy + elosvx2 + xy + y2)' equal to zero and attempt to solve:

Simplifying
-1elosvxy + elosvx2 + xy + y2 = 0

Solving
-1elosvxy + elosvx2 + xy + y2 = 0

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

Add 'elosvxy' to each side of the equation.
-1elosvxy + elosvx2 + xy + elosvxy + y2 = 0 + elosvxy

Reorder the terms:
-1elosvxy + elosvxy + elosvx2 + xy + y2 = 0 + elosvxy

Combine like terms: -1elosvxy + elosvxy = 0
0 + elosvx2 + xy + y2 = 0 + elosvxy
elosvx2 + xy + y2 = 0 + elosvxy
Remove the zero:
elosvx2 + xy + y2 = elosvxy

Add '-1elosvx2' to each side of the equation.
elosvx2 + xy + -1elosvx2 + y2 = elosvxy + -1elosvx2

Reorder the terms:
elosvx2 + -1elosvx2 + xy + y2 = elosvxy + -1elosvx2

Combine like terms: elosvx2 + -1elosvx2 = 0
0 + xy + y2 = elosvxy + -1elosvx2
xy + y2 = elosvxy + -1elosvx2

Add '-1xy' to each side of the equation.
xy + -1xy + y2 = elosvxy + -1elosvx2 + -1xy

Combine like terms: xy + -1xy = 0
0 + y2 = elosvxy + -1elosvx2 + -1xy
y2 = elosvxy + -1elosvx2 + -1xy

Add '-1y2' to each side of the equation.
y2 + -1y2 = elosvxy + -1elosvx2 + -1xy + -1y2

Combine like terms: y2 + -1y2 = 0
0 = elosvxy + -1elosvx2 + -1xy + -1y2

Simplifying
0 = elosvxy + -1elosvx2 + -1xy + -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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