(x+y)dx+xdy=0

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


Simplifying
(x + y) * dx + xdy = 0

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

Reorder the terms:
(dxy + dx2) + xdy = 0
(dxy + dx2) + xdy = 0

Reorder the terms:
dxy + dxy + dx2 = 0

Combine like terms: dxy + dxy = 2dxy
2dxy + dx2 = 0

Solving
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), 'dx'.
dx(2y + 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 '(2y + x)' equal to zero and attempt to solve:

Simplifying
2y + x = 0

Reorder the terms:
x + 2y = 0

Solving
x + 2y = 0

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

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

Combine like terms: x + -1x = 0
0 + 2y = 0 + -1x
2y = 0 + -1x
Remove the zero:
2y = -1x

Add '-2y' to each side of the equation.
2y + -2y = -1x + -2y

Combine like terms: 2y + -2y = 0
0 = -1x + -2y

Simplifying
0 = -1x + -2y

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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