Y(1+xy)dx+x(1-xy)=0

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Solution for Y(1+xy)dx+x(1-xy)=0 equation:


Simplifying
Y(1 + xy) * dx + x(1 + -1xy) = 0

Reorder the terms for easier multiplication:
Y * dx(1 + xy) + x(1 + -1xy) = 0

Multiply Y * dx
dxY(1 + xy) + x(1 + -1xy) = 0
(1 * dxY + xy * dxY) + x(1 + -1xy) = 0
(1dxY + dx2yY) + x(1 + -1xy) = 0
1dxY + dx2yY + (1 * x + -1xy * x) = 0
1dxY + dx2yY + (1x + -1x2y) = 0

Solving
1dxY + dx2yY + 1x + -1x2y = 0

Solving for variable 'd'.

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

Add '-1x' to each side of the equation.
1dxY + dx2yY + 1x + -1x + -1x2y = 0 + -1x

Combine like terms: 1x + -1x = 0
1dxY + dx2yY + 0 + -1x2y = 0 + -1x
1dxY + dx2yY + -1x2y = 0 + -1x
Remove the zero:
1dxY + dx2yY + -1x2y = -1x

Add 'x2y' to each side of the equation.
1dxY + dx2yY + -1x2y + x2y = -1x + x2y

Combine like terms: -1x2y + x2y = 0
1dxY + dx2yY + 0 = -1x + x2y
1dxY + dx2yY = -1x + x2y

Reorder the terms:
1dxY + dx2yY + x + -1x2y = -1x + x + x2y + -1x2y

Combine like terms: -1x + x = 0
1dxY + dx2yY + x + -1x2y = 0 + x2y + -1x2y
1dxY + dx2yY + x + -1x2y = x2y + -1x2y

Combine like terms: x2y + -1x2y = 0
1dxY + dx2yY + x + -1x2y = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(dY + dxyY + 1 + -1xy) = 0

Subproblem 1

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