(5x^2-9xy-y)dx+(6y-2x-x^2)dy=0

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Solution for (5x^2-9xy-y)dx+(6y-2x-x^2)dy=0 equation: 


Simplifying
(5x2 + -9xy + -1y) * dx + (6y + -2x + -1x2) * dy = 0

Reorder the terms:
(-9xy + 5x2 + -1y) * dx + (6y + -2x + -1x2) * dy = 0

Reorder the terms for easier multiplication:
dx(-9xy + 5x2 + -1y) + (6y + -2x + -1x2) * dy = 0
(-9xy * dx + 5x2 * dx + -1y * dx) + (6y + -2x + -1x2) * dy = 0

Reorder the terms:
(-1dxy + -9dx2y + 5dx3) + (6y + -2x + -1x2) * dy = 0
(-1dxy + -9dx2y + 5dx3) + (6y + -2x + -1x2) * dy = 0

Reorder the terms:
-1dxy + -9dx2y + 5dx3 + (-2x + -1x2 + 6y) * dy = 0

Reorder the terms for easier multiplication:
-1dxy + -9dx2y + 5dx3 + dy(-2x + -1x2 + 6y) = 0
-1dxy + -9dx2y + 5dx3 + (-2x * dy + -1x2 * dy + 6y * dy) = 0
-1dxy + -9dx2y + 5dx3 + (-2dxy + -1dx2y + 6dy2) = 0

Reorder the terms:
-1dxy + -2dxy + -9dx2y + -1dx2y + 5dx3 + 6dy2 = 0

Combine like terms: -1dxy + -2dxy = -3dxy
-3dxy + -9dx2y + -1dx2y + 5dx3 + 6dy2 = 0

Combine like terms: -9dx2y + -1dx2y = -10dx2y
-3dxy + -10dx2y + 5dx3 + 6dy2 = 0

Solving
-3dxy + -10dx2y + 5dx3 + 6dy2 = 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(-3xy + -10x2y + 5x3 + 6y2) = 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 '(-3xy + -10x2y + 5x3 + 6y2)' equal to zero and attempt to solve:

Simplifying
-3xy + -10x2y + 5x3 + 6y2 = 0

Solving
-3xy + -10x2y + 5x3 + 6y2 = 0

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

Add '3xy' to each side of the equation.
-3xy + -10x2y + 5x3 + 3xy + 6y2 = 0 + 3xy

Reorder the terms:
-3xy + 3xy + -10x2y + 5x3 + 6y2 = 0 + 3xy

Combine like terms: -3xy + 3xy = 0
0 + -10x2y + 5x3 + 6y2 = 0 + 3xy
-10x2y + 5x3 + 6y2 = 0 + 3xy
Remove the zero:
-10x2y + 5x3 + 6y2 = 3xy

Add '10x2y' to each side of the equation.
-10x2y + 5x3 + 10x2y + 6y2 = 3xy + 10x2y

Reorder the terms:
-10x2y + 10x2y + 5x3 + 6y2 = 3xy + 10x2y

Combine like terms: -10x2y + 10x2y = 0
0 + 5x3 + 6y2 = 3xy + 10x2y
5x3 + 6y2 = 3xy + 10x2y

Add '-5x3' to each side of the equation.
5x3 + -5x3 + 6y2 = 3xy + 10x2y + -5x3

Combine like terms: 5x3 + -5x3 = 0
0 + 6y2 = 3xy + 10x2y + -5x3
6y2 = 3xy + 10x2y + -5x3

Add '-6y2' to each side of the equation.
6y2 + -6y2 = 3xy + 10x2y + -5x3 + -6y2

Combine like terms: 6y2 + -6y2 = 0
0 = 3xy + 10x2y + -5x3 + -6y2

Simplifying
0 = 3xy + 10x2y + -5x3 + -6y2

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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