(x+y)dy+ydx=0

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


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

Reorder the terms for easier multiplication:
dy(x + y) + ydx = 0
(x * dy + y * dy) + ydx = 0
(dxy + dy2) + ydx = 0

Reorder the terms:
dxy + dxy + dy2 = 0

Combine like terms: dxy + dxy = 2dxy
2dxy + dy2 = 0

Solving
2dxy + 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), 'dy'.
dy(2x + y) = 0


Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve:

Simplifying
dy = 0

Solving
dy = 0

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

Simplifying
dy = 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 '(2x + y)' equal to zero and attempt to solve:

Simplifying
2x + y = 0

Solving
2x + y = 0

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

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

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

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

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

Simplifying
0 = -2x + -1y

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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