((x^2)*y+y+1)*dx+x(1+x^2)*dy=0

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Solution for ((x^2)*y+y+1)*dx+x(1+x^2)*dy=0 equation: 


Simplifying
((x2) * y + y + 1) * dx + x(1 + x2) * dy = 0

Multiply x2 * y
(x2y + y + 1) * dx + x(1 + x2) * dy = 0

Reorder the terms:
(1 + x2y + y) * dx + x(1 + x2) * dy = 0

Reorder the terms for easier multiplication:
dx(1 + x2y + y) + x(1 + x2) * dy = 0
(1 * dx + x2y * dx + y * dx) + x(1 + x2) * dy = 0

Reorder the terms:
(1dx + dxy + dx3y) + x(1 + x2) * dy = 0
(1dx + dxy + dx3y) + x(1 + x2) * dy = 0

Reorder the terms for easier multiplication:
1dx + dxy + dx3y + x * dy(1 + x2) = 0

Multiply x * dy
1dx + dxy + dx3y + dxy(1 + x2) = 0
1dx + dxy + dx3y + (1 * dxy + x2 * dxy) = 0
1dx + dxy + dx3y + (1dxy + dx3y) = 0

Reorder the terms:
1dx + dxy + 1dxy + dx3y + dx3y = 0

Combine like terms: dxy + 1dxy = 2dxy
1dx + 2dxy + dx3y + dx3y = 0

Combine like terms: dx3y + dx3y = 2dx3y
1dx + 2dxy + 2dx3y = 0

Solving
1dx + 2dxy + 2dx3y = 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), 'dx'.
dx(1 + 2y + 2x2y) = 0


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

Simplifying
dx = 0

Solving
dx = 0

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

Simplifying
dx = 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 '(1 + 2y + 2x2y)' equal to zero and attempt to solve:

Simplifying
1 + 2y + 2x2y = 0

Reorder the terms:
1 + 2x2y + 2y = 0

Solving
1 + 2x2y + 2y = 0

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

Add '-1' to each side of the equation.
1 + 2x2y + -1 + 2y = 0 + -1

Reorder the terms:
1 + -1 + 2x2y + 2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x2y + 2y = 0 + -1
2x2y + 2y = 0 + -1

Combine like terms: 0 + -1 = -1
2x2y + 2y = -1

Add '-2x2y' to each side of the equation.
2x2y + -2x2y + 2y = -1 + -2x2y

Combine like terms: 2x2y + -2x2y = 0
0 + 2y = -1 + -2x2y
2y = -1 + -2x2y

Add '-2y' to each side of the equation.
2y + -2y = -1 + -2x2y + -2y

Combine like terms: 2y + -2y = 0
0 = -1 + -2x2y + -2y

Simplifying
0 = -1 + -2x2y + -2y

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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