y*dx+2*(x+y)dy=0

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Solution for y*dx+2*(x+y)dy=0 equation: 


Simplifying
y * dx + 2(x + y) * dy = 0

Multiply y * dx
dxy + 2(x + y) * dy = 0

Reorder the terms for easier multiplication:
dxy + 2dy(x + y) = 0
dxy + (x * 2dy + y * 2dy) = 0
dxy + (2dxy + 2dy2) = 0

Combine like terms: dxy + 2dxy = 3dxy
3dxy + 2dy2 = 0

Solving
3dxy + 2dy2 = 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(3x + 2y) = 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 '(3x + 2y)' equal to zero and attempt to solve:

Simplifying
3x + 2y = 0

Solving
3x + 2y = 0

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

Add '-3x' to each side of the equation.
3x + -3x + 2y = 0 + -3x

Combine like terms: 3x + -3x = 0
0 + 2y = 0 + -3x
2y = 0 + -3x
Remove the zero:
2y = -3x

Add '-2y' to each side of the equation.
2y + -2y = -3x + -2y

Combine like terms: 2y + -2y = 0
0 = -3x + -2y

Simplifying
0 = -3x + -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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