for(x+y)dx+(x-y)dx=0

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


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

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

Multiply for * dx
dforx(x + y) + (x + -1y) * dx = 0
(x * dforx + y * dforx) + (x + -1y) * dx = 0

Reorder the terms:
(dforxy + dforx2) + (x + -1y) * dx = 0
(dforxy + dforx2) + (x + -1y) * dx = 0

Reorder the terms for easier multiplication:
dforxy + dforx2 + dx(x + -1y) = 0
dforxy + dforx2 + (x * dx + -1y * dx) = 0

Reorder the terms:
dforxy + dforx2 + (-1dxy + dx2) = 0
dforxy + dforx2 + (-1dxy + dx2) = 0

Solving
dforxy + dforx2 + -1dxy + 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), 'dx'.
dx(fory + forx + -1y + x) = 0

Subproblem 1

Set the factor 'dx' equal to zero and attempt to solve: Simplifying dx = 0 Solving dx = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(fory + forx + -1y + x)' equal to zero and attempt to solve: Simplifying fory + forx + -1y + x = 0 Reorder the terms: forx + fory + x + -1y = 0 Solving forx + fory + x + -1y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1forx' to each side of the equation. forx + fory + x + -1forx + -1y = 0 + -1forx Reorder the terms: forx + -1forx + fory + x + -1y = 0 + -1forx Combine like terms: forx + -1forx = 0 0 + fory + x + -1y = 0 + -1forx fory + x + -1y = 0 + -1forx Remove the zero: fory + x + -1y = -1forx Add '-1fory' to each side of the equation. fory + x + -1fory + -1y = -1forx + -1fory Reorder the terms: fory + -1fory + x + -1y = -1forx + -1fory Combine like terms: fory + -1fory = 0 0 + x + -1y = -1forx + -1fory x + -1y = -1forx + -1fory Add '-1x' to each side of the equation. x + -1x + -1y = -1forx + -1fory + -1x Combine like terms: x + -1x = 0 0 + -1y = -1forx + -1fory + -1x -1y = -1forx + -1fory + -1x Add 'y' to each side of the equation. -1y + y = -1forx + -1fory + -1x + y Combine like terms: -1y + y = 0 0 = -1forx + -1fory + -1x + y Simplifying 0 = -1forx + -1fory + -1x + y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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