(x+y)*(dx)+x*y*(dy)=0

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


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

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

Reorder the terms:
(dxy + dx2) + x * y(dy) = 0
(dxy + dx2) + x * y(dy) = 0

Multiply x * y
dxy + dx2 + xy * dy = 0

Multiply xy * dy
dxy + dx2 + dxy2 = 0

Reorder the terms:
dxy + dxy2 + dx2 = 0

Solving
dxy + dxy2 + 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(y + y2 + 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 '(y + y2 + x)' equal to zero and attempt to solve:

Simplifying
y + y2 + x = 0

Reorder the terms:
x + y + y2 = 0

Solving
x + y + y2 = 0

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

Add '-1x' to each side of the equation.
x + y + -1x + y2 = 0 + -1x

Reorder the terms:
x + -1x + y + y2 = 0 + -1x

Combine like terms: x + -1x = 0
0 + y + y2 = 0 + -1x
y + y2 = 0 + -1x
Remove the zero:
y + y2 = -1x

Add '-1y' to each side of the equation.
y + -1y + y2 = -1x + -1y

Combine like terms: y + -1y = 0
0 + y2 = -1x + -1y
y2 = -1x + -1y

Add '-1y2' to each side of the equation.
y2 + -1y2 = -1x + -1y + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -1x + -1y + -1y2

Simplifying
0 = -1x + -1y + -1y2

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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