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

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


Simplifying
y(x2 + -1y2 + 1) * dx + -1x(x2 + -1y2 + -1) * dy = 0

Reorder the terms:
y(1 + x2 + -1y2) * dx + -1x(x2 + -1y2 + -1) * dy = 0

Reorder the terms for easier multiplication:
y * dx(1 + x2 + -1y2) + -1x(x2 + -1y2 + -1) * dy = 0

Multiply y * dx
dxy(1 + x2 + -1y2) + -1x(x2 + -1y2 + -1) * dy = 0
(1 * dxy + x2 * dxy + -1y2 * dxy) + -1x(x2 + -1y2 + -1) * dy = 0

Reorder the terms:
(1dxy + -1dxy3 + dx3y) + -1x(x2 + -1y2 + -1) * dy = 0
(1dxy + -1dxy3 + dx3y) + -1x(x2 + -1y2 + -1) * dy = 0

Reorder the terms:
1dxy + -1dxy3 + dx3y + -1x(-1 + x2 + -1y2) * dy = 0

Reorder the terms for easier multiplication:
1dxy + -1dxy3 + dx3y + -1x * dy(-1 + x2 + -1y2) = 0

Multiply x * dy
1dxy + -1dxy3 + dx3y + -1dxy(-1 + x2 + -1y2) = 0
1dxy + -1dxy3 + dx3y + (-1 * -1dxy + x2 * -1dxy + -1y2 * -1dxy) = 0

Reorder the terms:
1dxy + -1dxy3 + dx3y + (1dxy + 1dxy3 + -1dx3y) = 0
1dxy + -1dxy3 + dx3y + (1dxy + 1dxy3 + -1dx3y) = 0

Reorder the terms:
1dxy + 1dxy + -1dxy3 + 1dxy3 + dx3y + -1dx3y = 0

Combine like terms: 1dxy + 1dxy = 2dxy
2dxy + -1dxy3 + 1dxy3 + dx3y + -1dx3y = 0

Combine like terms: -1dxy3 + 1dxy3 = 0
2dxy + 0 + dx3y + -1dx3y = 0
2dxy + dx3y + -1dx3y = 0

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

Solving
2dxy = 0

Solving for variable 'd'.

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

Divide each side by '2'.
dxy = 0

Simplifying
dxy = 0

The solution to this equation could not be determined.

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