(x^2+2xy)dx+xdy=0

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


Simplifying
(x2 + 2xy) * dx + xdy = 0

Reorder the terms:
(2xy + x2) * dx + xdy = 0

Reorder the terms for easier multiplication:
dx(2xy + x2) + xdy = 0
(2xy * dx + x2 * dx) + xdy = 0
(2dx2y + dx3) + xdy = 0

Reorder the terms:
dxy + 2dx2y + dx3 = 0

Solving
dxy + 2dx2y + dx3 = 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(y + 2xy + x2) = 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 '(y + 2xy + x2)' equal to zero and attempt to solve: Simplifying y + 2xy + x2 = 0 Reorder the terms: 2xy + x2 + y = 0 Solving 2xy + x2 + y = 0 Move all terms containing d to the left, all other terms to the right. Add '-2xy' to each side of the equation. 2xy + x2 + -2xy + y = 0 + -2xy Reorder the terms: 2xy + -2xy + x2 + y = 0 + -2xy Combine like terms: 2xy + -2xy = 0 0 + x2 + y = 0 + -2xy x2 + y = 0 + -2xy Remove the zero: x2 + y = -2xy Add '-1x2' to each side of the equation. x2 + -1x2 + y = -2xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + y = -2xy + -1x2 y = -2xy + -1x2 Add '-1y' to each side of the equation. y + -1y = -2xy + -1x2 + -1y Combine like terms: y + -1y = 0 0 = -2xy + -1x2 + -1y Simplifying 0 = -2xy + -1x2 + -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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