(2+x)dx-(3+x)dy=0

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Solution for (2+x)dx-(3+x)dy=0 equation: 


Simplifying
(2 + x) * dx + -1(3 + x) * dy = 0

Reorder the terms for easier multiplication:
dx(2 + x) + -1(3 + x) * dy = 0
(2 * dx + x * dx) + -1(3 + x) * dy = 0
(2dx + dx2) + -1(3 + x) * dy = 0

Reorder the terms for easier multiplication:
2dx + dx2 + -1dy(3 + x) = 0
2dx + dx2 + (3 * -1dy + x * -1dy) = 0

Reorder the terms:
2dx + dx2 + (-1dxy + -3dy) = 0
2dx + dx2 + (-1dxy + -3dy) = 0

Reorder the terms:
2dx + -1dxy + dx2 + -3dy = 0

Solving
2dx + -1dxy + dx2 + -3dy = 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(2x + -1xy + x2 + -3y) = 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 '(2x + -1xy + x2 + -3y)' equal to zero and attempt to solve:

Simplifying
2x + -1xy + x2 + -3y = 0

Solving
2x + -1xy + x2 + -3y = 0

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

Add '-2x' to each side of the equation.
2x + -1xy + x2 + -2x + -3y = 0 + -2x

Reorder the terms:
2x + -2x + -1xy + x2 + -3y = 0 + -2x

Combine like terms: 2x + -2x = 0
0 + -1xy + x2 + -3y = 0 + -2x
-1xy + x2 + -3y = 0 + -2x
Remove the zero:
-1xy + x2 + -3y = -2x

Add 'xy' to each side of the equation.
-1xy + x2 + xy + -3y = -2x + xy

Reorder the terms:
-1xy + xy + x2 + -3y = -2x + xy

Combine like terms: -1xy + xy = 0
0 + x2 + -3y = -2x + xy
x2 + -3y = -2x + xy

Add '-1x2' to each side of the equation.
x2 + -1x2 + -3y = -2x + xy + -1x2

Combine like terms: x2 + -1x2 = 0
0 + -3y = -2x + xy + -1x2
-3y = -2x + xy + -1x2

Add '3y' to each side of the equation.
-3y + 3y = -2x + xy + -1x2 + 3y

Combine like terms: -3y + 3y = 0
0 = -2x + xy + -1x2 + 3y

Simplifying
0 = -2x + xy + -1x2 + 3y

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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