(xy)dy-(x^2+3y^2)dy=0

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Solution for (xy)dy-(x^2+3y^2)dy=0 equation: 


Simplifying
(xy) * dy + -1(x2 + 3y2) * dy = 0

Multiply xy * dy
dxy2 + -1(x2 + 3y2) * dy = 0

Reorder the terms for easier multiplication:
dxy2 + -1dy(x2 + 3y2) = 0
dxy2 + (x2 * -1dy + 3y2 * -1dy) = 0
dxy2 + (-1dx2y + -3dy3) = 0

Solving
dxy2 + -1dx2y + -3dy3 = 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(xy + -1x2 + -3y2) = 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 '(xy + -1x2 + -3y2)' equal to zero and attempt to solve:

Simplifying
xy + -1x2 + -3y2 = 0

Solving
xy + -1x2 + -3y2 = 0

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

Add '-1xy' to each side of the equation.
xy + -1x2 + -1xy + -3y2 = 0 + -1xy

Reorder the terms:
xy + -1xy + -1x2 + -3y2 = 0 + -1xy

Combine like terms: xy + -1xy = 0
0 + -1x2 + -3y2 = 0 + -1xy
-1x2 + -3y2 = 0 + -1xy
Remove the zero:
-1x2 + -3y2 = -1xy

Add 'x2' to each side of the equation.
-1x2 + x2 + -3y2 = -1xy + x2

Combine like terms: -1x2 + x2 = 0
0 + -3y2 = -1xy + x2
-3y2 = -1xy + x2

Add '3y2' to each side of the equation.
-3y2 + 3y2 = -1xy + x2 + 3y2

Combine like terms: -3y2 + 3y2 = 0
0 = -1xy + x2 + 3y2

Simplifying
0 = -1xy + x2 + 3y2

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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