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

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


Simplifying
ydx + (xy2 + x + -1) * dy = 0

Reorder the terms:
dxy + (-1 + x + xy2) * dy = 0

Reorder the terms for easier multiplication:
dxy + dy(-1 + x + xy2) = 0
dxy + (-1 * dy + x * dy + xy2 * dy) = 0

Reorder the terms:
dxy + (dxy + dxy3 + -1dy) = 0
dxy + (dxy + dxy3 + -1dy) = 0

Combine like terms: dxy + dxy = 2dxy
2dxy + dxy3 + -1dy = 0

Solving
2dxy + dxy3 + -1dy = 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), 'dy'.
dy(2x + xy2 + -1) = 0


Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve:

Simplifying
dy = 0

Solving
dy = 0

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

Simplifying
dy = 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 '(2x + xy2 + -1)' equal to zero and attempt to solve:

Simplifying
2x + xy2 + -1 = 0

Reorder the terms:
-1 + 2x + xy2 = 0

Solving
-1 + 2x + xy2 = 0

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

Add '1' to each side of the equation.
-1 + 2x + 1 + xy2 = 0 + 1

Reorder the terms:
-1 + 1 + 2x + xy2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2x + xy2 = 0 + 1
2x + xy2 = 0 + 1

Combine like terms: 0 + 1 = 1
2x + xy2 = 1

Add '-2x' to each side of the equation.
2x + -2x + xy2 = 1 + -2x

Combine like terms: 2x + -2x = 0
0 + xy2 = 1 + -2x
xy2 = 1 + -2x

Add '-1xy2' to each side of the equation.
xy2 + -1xy2 = 1 + -2x + -1xy2

Combine like terms: xy2 + -1xy2 = 0
0 = 1 + -2x + -1xy2

Simplifying
0 = 1 + -2x + -1xy2

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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