(2x+y)dx+xdy=0

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


Simplifying
(2x + y) * dx + xdy = 0

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

Reorder the terms:
(dxy + 2dx2) + xdy = 0
(dxy + 2dx2) + xdy = 0

Reorder the terms:
dxy + dxy + 2dx2 = 0

Combine like terms: dxy + dxy = 2dxy
2dxy + 2dx2 = 0

Solving
2dxy + 2dx2 = 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), '2dx'.
2dx(y + x) = 0

Ignore the factor 2.

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 '(y + x)' equal to zero and attempt to solve: Simplifying y + x = 0 Reorder the terms: x + y = 0 Solving x + y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + y = 0 + -1x Combine like terms: x + -1x = 0 0 + y = 0 + -1x y = 0 + -1x Remove the zero: y = -1x Add '-1y' to each side of the equation. y + -1y = -1x + -1y Combine like terms: y + -1y = 0 0 = -1x + -1y Simplifying 0 = -1x + -1y 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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