(1+2y)dx-(4-x)dy=0

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Solution for (1+2y)dx-(4-x)dy=0 equation: 


Simplifying
(1 + 2y) * dx + -1(4 + -1x) * dy = 0

Reorder the terms for easier multiplication:
dx(1 + 2y) + -1(4 + -1x) * dy = 0
(1 * dx + 2y * dx) + -1(4 + -1x) * dy = 0
(1dx + 2dxy) + -1(4 + -1x) * dy = 0

Reorder the terms for easier multiplication:
1dx + 2dxy + -1dy(4 + -1x) = 0
1dx + 2dxy + (4 * -1dy + -1x * -1dy) = 0

Reorder the terms:
1dx + 2dxy + (1dxy + -4dy) = 0
1dx + 2dxy + (1dxy + -4dy) = 0

Combine like terms: 2dxy + 1dxy = 3dxy
1dx + 3dxy + -4dy = 0

Solving
1dx + 3dxy + -4dy = 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 + 3xy + -4y) = 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 + 3xy + -4y)' equal to zero and attempt to solve:

Simplifying
x + 3xy + -4y = 0

Solving
x + 3xy + -4y = 0

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

Add '-1x' to each side of the equation.
x + 3xy + -1x + -4y = 0 + -1x

Reorder the terms:
x + -1x + 3xy + -4y = 0 + -1x

Combine like terms: x + -1x = 0
0 + 3xy + -4y = 0 + -1x
3xy + -4y = 0 + -1x
Remove the zero:
3xy + -4y = -1x

Add '-3xy' to each side of the equation.
3xy + -3xy + -4y = -1x + -3xy

Combine like terms: 3xy + -3xy = 0
0 + -4y = -1x + -3xy
-4y = -1x + -3xy

Add '4y' to each side of the equation.
-4y + 4y = -1x + -3xy + 4y

Combine like terms: -4y + 4y = 0
0 = -1x + -3xy + 4y

Simplifying
0 = -1x + -3xy + 4y

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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