(x+y)dy+3dx=0

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Solution for (x+y)dy+3dx=0 equation: 


Simplifying
(x + y) * dy + 3dx = 0

Reorder the terms for easier multiplication:
dy(x + y) + 3dx = 0
(x * dy + y * dy) + 3dx = 0
(dxy + dy2) + 3dx = 0

Reorder the terms:
3dx + dxy + dy2 = 0

Solving
3dx + dxy + 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), 'd'.
d(3x + xy + y2) = 0


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

Simplifying
d = 0

Solving
d = 0

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

Simplifying
d = 0

Subproblem 2
Set the factor '(3x + xy + y2)' equal to zero and attempt to solve:

Simplifying
3x + xy + y2 = 0

Solving
3x + xy + y2 = 0

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

Add '-3x' to each side of the equation.
3x + xy + -3x + y2 = 0 + -3x

Reorder the terms:
3x + -3x + xy + y2 = 0 + -3x

Combine like terms: 3x + -3x = 0
0 + xy + y2 = 0 + -3x
xy + y2 = 0 + -3x
Remove the zero:
xy + y2 = -3x

Add '-1xy' to each side of the equation.
xy + -1xy + y2 = -3x + -1xy

Combine like terms: xy + -1xy = 0
0 + y2 = -3x + -1xy
y2 = -3x + -1xy

Add '-1y2' to each side of the equation.
y2 + -1y2 = -3x + -1xy + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -3x + -1xy + -1y2

Simplifying
0 = -3x + -1xy + -1y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}

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