(-x+y)dx+(7x-4y)dy=0

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Solution for (-x+y)dx+(7x-4y)dy=0 equation: 


Simplifying
(-1x + y) * dx + (7x + -4y) * dy = 0

Reorder the terms for easier multiplication:
dx(-1x + y) + (7x + -4y) * dy = 0
(-1x * dx + y * dx) + (7x + -4y) * dy = 0

Reorder the terms:
(dxy + -1dx2) + (7x + -4y) * dy = 0
(dxy + -1dx2) + (7x + -4y) * dy = 0

Reorder the terms for easier multiplication:
dxy + -1dx2 + dy(7x + -4y) = 0
dxy + -1dx2 + (7x * dy + -4y * dy) = 0
dxy + -1dx2 + (7dxy + -4dy2) = 0

Reorder the terms:
dxy + 7dxy + -1dx2 + -4dy2 = 0

Combine like terms: dxy + 7dxy = 8dxy
8dxy + -1dx2 + -4dy2 = 0

Solving
8dxy + -1dx2 + -4dy2 = 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(8xy + -1x2 + -4y2) = 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 '(8xy + -1x2 + -4y2)' equal to zero and attempt to solve:

Simplifying
8xy + -1x2 + -4y2 = 0

Solving
8xy + -1x2 + -4y2 = 0

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

Add '-8xy' to each side of the equation.
8xy + -1x2 + -8xy + -4y2 = 0 + -8xy

Reorder the terms:
8xy + -8xy + -1x2 + -4y2 = 0 + -8xy

Combine like terms: 8xy + -8xy = 0
0 + -1x2 + -4y2 = 0 + -8xy
-1x2 + -4y2 = 0 + -8xy
Remove the zero:
-1x2 + -4y2 = -8xy

Add 'x2' to each side of the equation.
-1x2 + x2 + -4y2 = -8xy + x2

Combine like terms: -1x2 + x2 = 0
0 + -4y2 = -8xy + x2
-4y2 = -8xy + x2

Add '4y2' to each side of the equation.
-4y2 + 4y2 = -8xy + x2 + 4y2

Combine like terms: -4y2 + 4y2 = 0
0 = -8xy + x2 + 4y2

Simplifying
0 = -8xy + x2 + 4y2

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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