(x+x*y^2)*dy+y*dx=0

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Solution for (x+x*y^2)*dy+y*dx=0 equation: 


Simplifying
(x + x * y2) * dy + y * dx = 0

Multiply x * y2
(x + xy2) * dy + y * dx = 0

Reorder the terms for easier multiplication:
dy(x + xy2) + y * dx = 0
(x * dy + xy2 * dy) + y * dx = 0
(dxy + dxy3) + y * dx = 0

Multiply y * dx
dxy + dxy3 + dxy = 0

Reorder the terms:
dxy + dxy + dxy3 = 0

Combine like terms: dxy + dxy = 2dxy
2dxy + dxy3 = 0

Solving
2dxy + dxy3 = 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 + y2) = 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 + y2)' equal to zero and attempt to solve:

Simplifying
2 + y2 = 0

Solving
2 + y2 = 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 + y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + y2 = 0 + -2
y2 = 0 + -2

Combine like terms: 0 + -2 = -2
y2 = -2

Add '-1y2' to each side of the equation.
y2 + -1y2 = -2 + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -2 + -1y2

Simplifying
0 = -2 + -1y2

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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