ydx+x(1+xy)dy=0

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Solution for ydx+x(1+xy)dy=0 equation:


Simplifying
ydx + x(1 + xy) * dy = 0

Reorder the terms for easier multiplication:
dxy + x * dy(1 + xy) = 0

Multiply x * dy
dxy + dxy(1 + xy) = 0
dxy + (1 * dxy + xy * dxy) = 0
dxy + (1dxy + dx2y2) = 0

Combine like terms: dxy + 1dxy = 2dxy
2dxy + dx2y2 = 0

Solving
2dxy + dx2y2 = 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), 'dxy'.
dxy(2 + xy) = 0

Subproblem 1

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