(x^2-4)dy+dx=4dx

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


Simplifying
(x2 + -4) * dy + dx = 4dx

Reorder the terms:
(-4 + x2) * dy + dx = 4dx

Reorder the terms for easier multiplication:
dy(-4 + x2) + dx = 4dx
(-4 * dy + x2 * dy) + dx = 4dx

Reorder the terms:
(dx2y + -4dy) + dx = 4dx
(dx2y + -4dy) + dx = 4dx

Reorder the terms:
dx + dx2y + -4dy = 4dx

Solving
dx + dx2y + -4dy = 4dx

Solving for variable 'd'.

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

Add '-4dx' to each side of the equation.
dx + dx2y + -4dx + -4dy = 4dx + -4dx

Reorder the terms:
dx + -4dx + dx2y + -4dy = 4dx + -4dx

Combine like terms: dx + -4dx = -3dx
-3dx + dx2y + -4dy = 4dx + -4dx

Combine like terms: 4dx + -4dx = 0
-3dx + dx2y + -4dy = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(-3x + x2y + -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 '(-3x + x2y + -4y)' equal to zero and attempt to solve:

Simplifying
-3x + x2y + -4y = 0

Solving
-3x + x2y + -4y = 0

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

Add '3x' to each side of the equation.
-3x + x2y + 3x + -4y = 0 + 3x

Reorder the terms:
-3x + 3x + x2y + -4y = 0 + 3x

Combine like terms: -3x + 3x = 0
0 + x2y + -4y = 0 + 3x
x2y + -4y = 0 + 3x
Remove the zero:
x2y + -4y = 3x

Add '-1x2y' to each side of the equation.
x2y + -1x2y + -4y = 3x + -1x2y

Combine like terms: x2y + -1x2y = 0
0 + -4y = 3x + -1x2y
-4y = 3x + -1x2y

Add '4y' to each side of the equation.
-4y + 4y = 3x + -1x2y + 4y

Combine like terms: -4y + 4y = 0
0 = 3x + -1x2y + 4y

Simplifying
0 = 3x + -1x2y + 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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