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

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


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

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

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

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

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

Solving
-2dvx + 2dxy + dx2 + dy2 = 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(-2vx + 2xy + x2 + y2) = 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 '(-2vx + 2xy + x2 + y2)' equal to zero and attempt to solve: Simplifying -2vx + 2xy + x2 + y2 = 0 Solving -2vx + 2xy + x2 + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '2vx' to each side of the equation. -2vx + 2xy + x2 + 2vx + y2 = 0 + 2vx Reorder the terms: -2vx + 2vx + 2xy + x2 + y2 = 0 + 2vx Combine like terms: -2vx + 2vx = 0 0 + 2xy + x2 + y2 = 0 + 2vx 2xy + x2 + y2 = 0 + 2vx Remove the zero: 2xy + x2 + y2 = 2vx Add '-2xy' to each side of the equation. 2xy + x2 + -2xy + y2 = 2vx + -2xy Reorder the terms: 2xy + -2xy + x2 + y2 = 2vx + -2xy Combine like terms: 2xy + -2xy = 0 0 + x2 + y2 = 2vx + -2xy x2 + y2 = 2vx + -2xy Add '-1x2' to each side of the equation. x2 + -1x2 + y2 = 2vx + -2xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + y2 = 2vx + -2xy + -1x2 y2 = 2vx + -2xy + -1x2 Add '-1y2' to each side of the equation. y2 + -1y2 = 2vx + -2xy + -1x2 + -1y2 Combine like terms: y2 + -1y2 = 0 0 = 2vx + -2xy + -1x2 + -1y2 Simplifying 0 = 2vx + -2xy + -1x2 + -1y2 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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