(1+lnx)dx+(1+lny)dy=0

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Solution for (1+lnx)dx+(1+lny)dy=0 equation: 


Simplifying
(1 + lnx) * dx + (1 + lny) * dy = 0

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

Reorder the terms:
(dlnx2 + 1dx) + (1 + lny) * dy = 0
(dlnx2 + 1dx) + (1 + lny) * dy = 0

Reorder the terms for easier multiplication:
dlnx2 + 1dx + dy(1 + lny) = 0
dlnx2 + 1dx + (1 * dy + lny * dy) = 0

Reorder the terms:
dlnx2 + 1dx + (dlny2 + 1dy) = 0
dlnx2 + 1dx + (dlny2 + 1dy) = 0

Reorder the terms:
dlnx2 + dlny2 + 1dx + 1dy = 0

Solving
dlnx2 + dlny2 + 1dx + 1dy = 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), 'd'.
d(lnx2 + lny2 + x + y) = 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 '(lnx2 + lny2 + x + y)' equal to zero and attempt to solve:

Simplifying
lnx2 + lny2 + x + y = 0

Solving
lnx2 + lny2 + x + y = 0

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

Add '-1lnx2' to each side of the equation.
lnx2 + lny2 + x + -1lnx2 + y = 0 + -1lnx2

Reorder the terms:
lnx2 + -1lnx2 + lny2 + x + y = 0 + -1lnx2

Combine like terms: lnx2 + -1lnx2 = 0
0 + lny2 + x + y = 0 + -1lnx2
lny2 + x + y = 0 + -1lnx2
Remove the zero:
lny2 + x + y = -1lnx2

Add '-1lny2' to each side of the equation.
lny2 + x + -1lny2 + y = -1lnx2 + -1lny2

Reorder the terms:
lny2 + -1lny2 + x + y = -1lnx2 + -1lny2

Combine like terms: lny2 + -1lny2 = 0
0 + x + y = -1lnx2 + -1lny2
x + y = -1lnx2 + -1lny2

Add '-1x' to each side of the equation.
x + -1x + y = -1lnx2 + -1lny2 + -1x

Combine like terms: x + -1x = 0
0 + y = -1lnx2 + -1lny2 + -1x
y = -1lnx2 + -1lny2 + -1x

Add '-1y' to each side of the equation.
y + -1y = -1lnx2 + -1lny2 + -1x + -1y

Combine like terms: y + -1y = 0
0 = -1lnx2 + -1lny2 + -1x + -1y

Simplifying
0 = -1lnx2 + -1lny2 + -1x + -1y

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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