(7x+y)dx+(2x-y)dy=0

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Solution for (7x+y)dx+(2x-y)dy=0 equation: 


Simplifying
(7x + y) * dx + (2x + -1y) * dy = 0

Reorder the terms for easier multiplication:
dx(7x + y) + (2x + -1y) * dy = 0
(7x * dx + y * dx) + (2x + -1y) * dy = 0

Reorder the terms:
(dxy + 7dx2) + (2x + -1y) * dy = 0
(dxy + 7dx2) + (2x + -1y) * dy = 0

Reorder the terms for easier multiplication:
dxy + 7dx2 + dy(2x + -1y) = 0
dxy + 7dx2 + (2x * dy + -1y * dy) = 0
dxy + 7dx2 + (2dxy + -1dy2) = 0

Reorder the terms:
dxy + 2dxy + 7dx2 + -1dy2 = 0

Combine like terms: dxy + 2dxy = 3dxy
3dxy + 7dx2 + -1dy2 = 0

Solving
3dxy + 7dx2 + -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(3xy + 7x2 + -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 '(3xy + 7x2 + -1y2)' equal to zero and attempt to solve:

Simplifying
3xy + 7x2 + -1y2 = 0

Solving
3xy + 7x2 + -1y2 = 0

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

Add '-3xy' to each side of the equation.
3xy + 7x2 + -3xy + -1y2 = 0 + -3xy

Reorder the terms:
3xy + -3xy + 7x2 + -1y2 = 0 + -3xy

Combine like terms: 3xy + -3xy = 0
0 + 7x2 + -1y2 = 0 + -3xy
7x2 + -1y2 = 0 + -3xy
Remove the zero:
7x2 + -1y2 = -3xy

Add '-7x2' to each side of the equation.
7x2 + -7x2 + -1y2 = -3xy + -7x2

Combine like terms: 7x2 + -7x2 = 0
0 + -1y2 = -3xy + -7x2
-1y2 = -3xy + -7x2

Add 'y2' to each side of the equation.
-1y2 + y2 = -3xy + -7x2 + y2

Combine like terms: -1y2 + y2 = 0
0 = -3xy + -7x2 + y2

Simplifying
0 = -3xy + -7x2 + 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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