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

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


Simplifying
(xy + -4x) * dx + (x2y + y) * dy = 0

Reorder the terms:
(-4x + xy) * dx + (x2y + y) * dy = 0

Reorder the terms for easier multiplication:
dx(-4x + xy) + (x2y + y) * dy = 0
(-4x * dx + xy * dx) + (x2y + y) * dy = 0
(-4dx2 + dx2y) + (x2y + y) * dy = 0

Reorder the terms for easier multiplication:
-4dx2 + dx2y + dy(x2y + y) = 0
-4dx2 + dx2y + (x2y * dy + y * dy) = 0
-4dx2 + dx2y + (dx2y2 + dy2) = 0

Solving
-4dx2 + dx2y + dx2y2 + dy2 = 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(-4x2 + x2y + x2y2 + y2) = 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 '(-4x2 + x2y + x2y2 + y2)' equal to zero and attempt to solve:

Simplifying
-4x2 + x2y + x2y2 + y2 = 0

Solving
-4x2 + x2y + x2y2 + y2 = 0

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

Add '4x2' to each side of the equation.
-4x2 + x2y + x2y2 + 4x2 + y2 = 0 + 4x2

Reorder the terms:
-4x2 + 4x2 + x2y + x2y2 + y2 = 0 + 4x2

Combine like terms: -4x2 + 4x2 = 0
0 + x2y + x2y2 + y2 = 0 + 4x2
x2y + x2y2 + y2 = 0 + 4x2
Remove the zero:
x2y + x2y2 + y2 = 4x2

Add '-1x2y' to each side of the equation.
x2y + x2y2 + -1x2y + y2 = 4x2 + -1x2y

Reorder the terms:
x2y + -1x2y + x2y2 + y2 = 4x2 + -1x2y

Combine like terms: x2y + -1x2y = 0
0 + x2y2 + y2 = 4x2 + -1x2y
x2y2 + y2 = 4x2 + -1x2y

Add '-1x2y2' to each side of the equation.
x2y2 + -1x2y2 + y2 = 4x2 + -1x2y + -1x2y2

Combine like terms: x2y2 + -1x2y2 = 0
0 + y2 = 4x2 + -1x2y + -1x2y2
y2 = 4x2 + -1x2y + -1x2y2

Add '-1y2' to each side of the equation.
y2 + -1y2 = 4x2 + -1x2y + -1x2y2 + -1y2

Combine like terms: y2 + -1y2 = 0
0 = 4x2 + -1x2y + -1x2y2 + -1y2

Simplifying
0 = 4x2 + -1x2y + -1x2y2 + -1y2

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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