dx-xdy=ln(y)dy

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Solution for dx-xdy=ln(y)dy equation: 


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

Multiply ln * y
dx + -1dxy = lny * dy

Multiply lny * dy
dx + -1dxy = dlny2

Solving
dx + -1dxy = dlny2

Solving for variable 'd'.

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

Add '-1dlny2' to each side of the equation.
dx + -1dlny2 + -1dxy = dlny2 + -1dlny2

Reorder the terms:
-1dlny2 + dx + -1dxy = dlny2 + -1dlny2

Combine like terms: dlny2 + -1dlny2 = 0
-1dlny2 + dx + -1dxy = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(-1lny2 + x + -1xy) = 0


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

Simplifying
d = 0

Solving
d = 0

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

Simplifying
d = 0

Subproblem 2
Set the factor '(-1lny2 + x + -1xy)' equal to zero and attempt to solve:

Simplifying
-1lny2 + x + -1xy = 0

Solving
-1lny2 + x + -1xy = 0

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

Add 'lny2' to each side of the equation.
-1lny2 + x + lny2 + -1xy = 0 + lny2

Reorder the terms:
-1lny2 + lny2 + x + -1xy = 0 + lny2

Combine like terms: -1lny2 + lny2 = 0
0 + x + -1xy = 0 + lny2
x + -1xy = 0 + lny2
Remove the zero:
x + -1xy = lny2

Add '-1x' to each side of the equation.
x + -1x + -1xy = lny2 + -1x

Combine like terms: x + -1x = 0
0 + -1xy = lny2 + -1x
-1xy = lny2 + -1x

Add 'xy' to each side of the equation.
-1xy + xy = lny2 + -1x + xy

Combine like terms: -1xy + xy = 0
0 = lny2 + -1x + xy

Simplifying
0 = lny2 + -1x + xy

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}

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