dx+(x+10y)dy=0

Solution for dx+(x+10y)dy=0 equation:

Simplifying
dx + (x + 10y) * dy = 0

Reorder the terms for easier multiplication:
dx + dy(x + 10y) = 0
dx + (x * dy + 10y * dy) = 0
dx + (dxy + 10dy2) = 0

Solving
dx + dxy + 10dy2 = 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(x + xy + 10y2) = 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 '(x + xy + 10y2)' equal to zero and attempt to solve:

Simplifying
x + xy + 10y2 = 0

Solving
x + xy + 10y2 = 0

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

Add '-1x' to each side of the equation.
x + xy + -1x + 10y2 = 0 + -1x

Reorder the terms:
x + -1x + xy + 10y2 = 0 + -1x

Combine like terms: x + -1x = 0
0 + xy + 10y2 = 0 + -1x
xy + 10y2 = 0 + -1x
Remove the zero:
xy + 10y2 = -1x

Add '-1xy' to each side of the equation.
xy + -1xy + 10y2 = -1x + -1xy

Combine like terms: xy + -1xy = 0
0 + 10y2 = -1x + -1xy
10y2 = -1x + -1xy

Add '-10y2' to each side of the equation.
10y2 + -10y2 = -1x + -1xy + -10y2

Combine like terms: 10y2 + -10y2 = 0
0 = -1x + -1xy + -10y2

Simplifying
0 = -1x + -1xy + -10y2

The solution to this equation could not be determined.

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