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

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


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

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

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

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

Reorder the terms for easier multiplication:
dxy + dx2 + -1dy(-1t + x) = 0
dxy + dx2 + (-1t * -1dy + x * -1dy) = 0
dxy + dx2 + (1dty + -1dxy) = 0

Reorder the terms:
1dty + dxy + -1dxy + dx2 = 0

Combine like terms: dxy + -1dxy = 0
1dty + 0 + dx2 = 0
1dty + dx2 = 0

Solving
1dty + 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(ty + 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 '(ty + x2)' equal to zero and attempt to solve:

Simplifying
ty + x2 = 0

Solving
ty + x2 = 0

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

Add '-1ty' to each side of the equation.
ty + -1ty + x2 = 0 + -1ty

Combine like terms: ty + -1ty = 0
0 + x2 = 0 + -1ty
x2 = 0 + -1ty
Remove the zero:
x2 = -1ty

Add '-1x2' to each side of the equation.
x2 + -1x2 = -1ty + -1x2

Combine like terms: x2 + -1x2 = 0
0 = -1ty + -1x2

Simplifying
0 = -1ty + -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}

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