(y(ln(x)-ln(y)))dx-(xln(x)-xln(y)-y)dy=0

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


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

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

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

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

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

Multiply lnx * x
-1dlnxy2 + dlnx2y + -1(lnx2 + -1xln(y) + -1y) * dy = 0

Multiply lnx * y
-1dlnxy2 + dlnx2y + -1(lnx2 + -1lnxy + -1y) * dy = 0

Reorder the terms:
-1dlnxy2 + dlnx2y + -1(-1lnxy + lnx2 + -1y) * dy = 0

Reorder the terms for easier multiplication:
-1dlnxy2 + dlnx2y + -1dy(-1lnxy + lnx2 + -1y) = 0
-1dlnxy2 + dlnx2y + (-1lnxy * -1dy + lnx2 * -1dy + -1y * -1dy) = 0
-1dlnxy2 + dlnx2y + (1dlnxy2 + -1dlnx2y + 1dy2) = 0

Reorder the terms:
-1dlnxy2 + 1dlnxy2 + dlnx2y + -1dlnx2y + 1dy2 = 0

Combine like terms: -1dlnxy2 + 1dlnxy2 = 0
0 + dlnx2y + -1dlnx2y + 1dy2 = 0
dlnx2y + -1dlnx2y + 1dy2 = 0

Combine like terms: dlnx2y + -1dlnx2y = 0
0 + 1dy2 = 0
1dy2 = 0

Solving
1dy2 = 0

Solving for variable 'd'.

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

Divide each side by '1'.
dy2 = 0

Simplifying
dy2 = 0

The solution to this equation could not be determined.

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