(x-y)dy-3dx=0

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


Simplifying
(x + -1y) * dy + -3dx = 0

Reorder the terms for easier multiplication:
dy(x + -1y) + -3dx = 0
(x * dy + -1y * dy) + -3dx = 0
(dxy + -1dy2) + -3dx = 0

Reorder the terms:
-3dx + dxy + -1dy2 = 0

Solving
-3dx + dxy + -1dy2 = 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 + -1y2) = 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 + -1y2)' equal to zero and attempt to solve:

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

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

Reorder the terms:
-3x + 3x + xy + -1y2 = 0 + 3x

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

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

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

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

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

Simplifying
0 = 3x + -1xy + y2

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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