2xy+(x^2-1)dy=0

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Solution for 2xy+(x^2-1)dy=0 equation:


Simplifying
2xy + (x2 + -1) * dy = 0

Reorder the terms:
2xy + (-1 + x2) * dy = 0

Reorder the terms for easier multiplication:
2xy + dy(-1 + x2) = 0
2xy + (-1 * dy + x2 * dy) = 0

Reorder the terms:
2xy + (dx2y + -1dy) = 0
2xy + (dx2y + -1dy) = 0

Reorder the terms:
dx2y + -1dy + 2xy = 0

Solving
dx2y + -1dy + 2xy = 0

Solving for variable 'd'.

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

Add '-2xy' to each side of the equation.
dx2y + -1dy + 2xy + -2xy = 0 + -2xy

Combine like terms: 2xy + -2xy = 0
dx2y + -1dy + 0 = 0 + -2xy
dx2y + -1dy = 0 + -2xy
Remove the zero:
dx2y + -1dy = -2xy

Combine like terms: -2xy + 2xy = 0
dx2y + -1dy + 2xy = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(dx2 + -1d + 2x) = 0

Subproblem 1

Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1y' to each side of the equation. y + -1y = 0 + -1y Remove the zero: 0 = -1y Simplifying 0 = -1y 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 '(dx2 + -1d + 2x)' equal to zero and attempt to solve: Simplifying dx2 + -1d + 2x = 0 Reorder the terms: -1d + dx2 + 2x = 0 Solving -1d + dx2 + 2x = 0 Move all terms containing d to the left, all other terms to the right. Add '-2x' to each side of the equation. -1d + dx2 + 2x + -2x = 0 + -2x Combine like terms: 2x + -2x = 0 -1d + dx2 + 0 = 0 + -2x -1d + dx2 = 0 + -2x Remove the zero: -1d + dx2 = -2x 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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