y(y^2+1)dx+x(y^3-1)dy=0

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Solution for y(y^2+1)dx+x(y^3-1)dy=0 equation: 


Simplifying
y(y2 + 1) * dx + x(y3 + -1) * dy = 0

Reorder the terms:
y(1 + y2) * dx + x(y3 + -1) * dy = 0

Reorder the terms for easier multiplication:
y * dx(1 + y2) + x(y3 + -1) * dy = 0

Multiply y * dx
dxy(1 + y2) + x(y3 + -1) * dy = 0
(1 * dxy + y2 * dxy) + x(y3 + -1) * dy = 0
(1dxy + dxy3) + x(y3 + -1) * dy = 0

Reorder the terms:
1dxy + dxy3 + x(-1 + y3) * dy = 0

Reorder the terms for easier multiplication:
1dxy + dxy3 + x * dy(-1 + y3) = 0

Multiply x * dy
1dxy + dxy3 + dxy(-1 + y3) = 0
1dxy + dxy3 + (-1 * dxy + y3 * dxy) = 0
1dxy + dxy3 + (-1dxy + dxy4) = 0

Reorder the terms:
1dxy + -1dxy + dxy3 + dxy4 = 0

Combine like terms: 1dxy + -1dxy = 0
0 + dxy3 + dxy4 = 0
dxy3 + dxy4 = 0

Solving
dxy3 + dxy4 = 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), 'dxy3'.
dxy3(1 + y) = 0


Subproblem 1
Set the factor 'dxy3' equal to zero and attempt to solve:

Simplifying
dxy3 = 0

Solving
dxy3 = 0

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

Simplifying
dxy3 = 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 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

Solving
1 + y = 0

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

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

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

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

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

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

Simplifying
0 = -1 + -1y

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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