(x+y)dx+3xdy=0

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Solution for (x+y)dx+3xdy=0 equation:


Simplifying
(x + y) * dx + 3xdy = 0

Reorder the terms for easier multiplication:
dx(x + y) + 3xdy = 0
(x * dx + y * dx) + 3xdy = 0

Reorder the terms:
(dxy + dx2) + 3xdy = 0
(dxy + dx2) + 3xdy = 0

Reorder the terms:
dxy + 3dxy + dx2 = 0

Combine like terms: dxy + 3dxy = 4dxy
4dxy + dx2 = 0

Solving
4dxy + dx2 = 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), 'dx'.
dx(4y + x) = 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 '(4y + x)' equal to zero and attempt to solve: Simplifying 4y + x = 0 Reorder the terms: x + 4y = 0 Solving x + 4y = 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 + 4y = 0 + -1x Combine like terms: x + -1x = 0 0 + 4y = 0 + -1x 4y = 0 + -1x Remove the zero: 4y = -1x Add '-4y' to each side of the equation. 4y + -4y = -1x + -4y Combine like terms: 4y + -4y = 0 0 = -1x + -4y Simplifying 0 = -1x + -4y 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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