(x-y*ln(y)+y*ln(x))dx+x(ln(y)-ln(x))dy=0

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Solution for (x-y*ln(y)+y*ln(x))dx+x(ln(y)-ln(x))dy=0 equation: 


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

Multiply y * ln
(x + -1lny * y + y * ln(x)) * dx + x(ln(y) + -1ln(x)) * dy = 0

Multiply lny * y
(x + -1lny2 + y * ln(x)) * dx + x(ln(y) + -1ln(x)) * dy = 0

Multiply y * ln
(x + -1lny2 + lny * x) * dx + x(ln(y) + -1ln(x)) * dy = 0

Multiply lny * x
(x + -1lny2 + lnxy) * dx + x(ln(y) + -1ln(x)) * dy = 0

Reorder the terms:
(lnxy + -1lny2 + x) * dx + x(ln(y) + -1ln(x)) * dy = 0

Reorder the terms for easier multiplication:
dx(lnxy + -1lny2 + x) + x(ln(y) + -1ln(x)) * dy = 0
(lnxy * dx + -1lny2 * dx + x * dx) + x(ln(y) + -1ln(x)) * dy = 0

Reorder the terms:
(-1dlnxy2 + dlnx2y + dx2) + x(ln(y) + -1ln(x)) * dy = 0
(-1dlnxy2 + dlnx2y + dx2) + x(ln(y) + -1ln(x)) * dy = 0

Multiply ln * y
-1dlnxy2 + dlnx2y + dx2 + x(lny + -1ln(x)) * dy = 0

Multiply ln * x
-1dlnxy2 + dlnx2y + dx2 + x(lny + -1lnx) * dy = 0

Reorder the terms:
-1dlnxy2 + dlnx2y + dx2 + x(-1lnx + lny) * dy = 0

Reorder the terms for easier multiplication:
-1dlnxy2 + dlnx2y + dx2 + x * dy(-1lnx + lny) = 0

Multiply x * dy
-1dlnxy2 + dlnx2y + dx2 + dxy(-1lnx + lny) = 0
-1dlnxy2 + dlnx2y + dx2 + (-1lnx * dxy + lny * dxy) = 0

Reorder the terms:
-1dlnxy2 + dlnx2y + dx2 + (dlnxy2 + -1dlnx2y) = 0
-1dlnxy2 + dlnx2y + dx2 + (dlnxy2 + -1dlnx2y) = 0

Reorder the terms:
-1dlnxy2 + dlnxy2 + dlnx2y + -1dlnx2y + dx2 = 0

Combine like terms: -1dlnxy2 + dlnxy2 = 0
0 + dlnx2y + -1dlnx2y + dx2 = 0
dlnx2y + -1dlnx2y + dx2 = 0

Combine like terms: dlnx2y + -1dlnx2y = 0
0 + dx2 = 0
dx2 = 0

Solving
dx2 = 0

Solving for variable 'd'.

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

Simplifying
dx2 = 0

The solution to this equation could not be determined.

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