(3x-y-5)dx+(x-y+1)dy=0

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Solution for (3x-y-5)dx+(x-y+1)dy=0 equation: 


Simplifying
(3x + -1y + -5) * dx + (x + -1y + 1) * dy = 0

Reorder the terms:
(-5 + 3x + -1y) * dx + (x + -1y + 1) * dy = 0

Reorder the terms for easier multiplication:
dx(-5 + 3x + -1y) + (x + -1y + 1) * dy = 0
(-5 * dx + 3x * dx + -1y * dx) + (x + -1y + 1) * dy = 0

Reorder the terms:
(-5dx + -1dxy + 3dx2) + (x + -1y + 1) * dy = 0
(-5dx + -1dxy + 3dx2) + (x + -1y + 1) * dy = 0

Reorder the terms:
-5dx + -1dxy + 3dx2 + (1 + x + -1y) * dy = 0

Reorder the terms for easier multiplication:
-5dx + -1dxy + 3dx2 + dy(1 + x + -1y) = 0
-5dx + -1dxy + 3dx2 + (1 * dy + x * dy + -1y * dy) = 0

Reorder the terms:
-5dx + -1dxy + 3dx2 + (dxy + 1dy + -1dy2) = 0
-5dx + -1dxy + 3dx2 + (dxy + 1dy + -1dy2) = 0

Reorder the terms:
-5dx + -1dxy + dxy + 3dx2 + 1dy + -1dy2 = 0

Combine like terms: -1dxy + dxy = 0
-5dx + 0 + 3dx2 + 1dy + -1dy2 = 0
-5dx + 3dx2 + 1dy + -1dy2 = 0

Solving
-5dx + 3dx2 + 1dy + -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(-5x + 3x2 + y + -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 '(-5x + 3x2 + y + -1y2)' equal to zero and attempt to solve:

Simplifying
-5x + 3x2 + y + -1y2 = 0

Solving
-5x + 3x2 + y + -1y2 = 0

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

Add '5x' to each side of the equation.
-5x + 3x2 + y + 5x + -1y2 = 0 + 5x

Reorder the terms:
-5x + 5x + 3x2 + y + -1y2 = 0 + 5x

Combine like terms: -5x + 5x = 0
0 + 3x2 + y + -1y2 = 0 + 5x
3x2 + y + -1y2 = 0 + 5x
Remove the zero:
3x2 + y + -1y2 = 5x

Add '-3x2' to each side of the equation.
3x2 + y + -3x2 + -1y2 = 5x + -3x2

Reorder the terms:
3x2 + -3x2 + y + -1y2 = 5x + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + y + -1y2 = 5x + -3x2
y + -1y2 = 5x + -3x2

Add '-1y' to each side of the equation.
y + -1y + -1y2 = 5x + -3x2 + -1y

Combine like terms: y + -1y = 0
0 + -1y2 = 5x + -3x2 + -1y
-1y2 = 5x + -3x2 + -1y

Add 'y2' to each side of the equation.
-1y2 + y2 = 5x + -3x2 + -1y + y2

Combine like terms: -1y2 + y2 = 0
0 = 5x + -3x2 + -1y + y2

Simplifying
0 = 5x + -3x2 + -1y + 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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