ydx-x(lnx-lny)dy=0

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Solution for ydx-x(lnx-lny)dy=0 equation: 


Simplifying
ydx + -1x(lnx + -1lny) * dy = 0

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

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

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

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

Solving
1dlnxy2 + -1dlnx2y + dxy = 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), 'dxy'.
dxy(lny + -1lnx + 1) = 0


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

Simplifying
dxy = 0

Solving
dxy = 0

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

Simplifying
dxy = 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 '(lny + -1lnx + 1)' equal to zero and attempt to solve:

Simplifying
lny + -1lnx + 1 = 0

Reorder the terms:
1 + -1lnx + lny = 0

Solving
1 + -1lnx + lny = 0

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

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

Reorder the terms:
1 + -1 + -1lnx + lny = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1lnx + lny = 0 + -1
-1lnx + lny = 0 + -1

Combine like terms: 0 + -1 = -1
-1lnx + lny = -1

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

Combine like terms: -1lnx + lnx = 0
0 + lny = -1 + lnx
lny = -1 + lnx

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

Combine like terms: lny + -1lny = 0
0 = -1 + lnx + -1lny

Simplifying
0 = -1 + lnx + -1lny

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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