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

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


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

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

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

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

Multiply dx * dy
-1dxy + 2dx2 + d2xy(x + y) = 0
-1dxy + 2dx2 + (x * d2xy + y * d2xy) = 0

Reorder the terms:
-1dxy + 2dx2 + (d2xy2 + d2x2y) = 0
-1dxy + 2dx2 + (d2xy2 + d2x2y) = 0

Solving
-1dxy + 2dx2 + d2xy2 + d2x2y = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), 'dx'.
dx(-1y + 2x + dy2 + dxy) = 0


Subproblem 1
Set the factor 'dx' equal to zero and attempt to solve:

Simplifying
dx = 0

Solving
dx = 0

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

Simplifying
dx = 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 '(-1y + 2x + dy2 + dxy)' equal to zero and attempt to solve:

Simplifying
-1y + 2x + dy2 + dxy = 0

Reorder the terms:
dxy + dy2 + 2x + -1y = 0

Solving
dxy + dy2 + 2x + -1y = 0

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

Add '-2x' to each side of the equation.
dxy + dy2 + 2x + -2x + -1y = 0 + -2x

Combine like terms: 2x + -2x = 0
dxy + dy2 + 0 + -1y = 0 + -2x
dxy + dy2 + -1y = 0 + -2x
Remove the zero:
dxy + dy2 + -1y = -2x

Add 'y' to each side of the equation.
dxy + dy2 + -1y + y = -2x + y

Combine like terms: -1y + y = 0
dxy + dy2 + 0 = -2x + y
dxy + dy2 = -2x + y

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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