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

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


Simplifying
(x * y) * dx + (x2 + -4) * dy = 0

Multiply x * y
(xy) * dx + (x2 + -4) * dy = 0

Multiply xy * dx
dx2y + (x2 + -4) * dy = 0

Reorder the terms:
dx2y + (-4 + x2) * dy = 0

Reorder the terms for easier multiplication:
dx2y + dy(-4 + x2) = 0
dx2y + (-4 * dy + x2 * dy) = 0

Reorder the terms:
dx2y + (dx2y + -4dy) = 0
dx2y + (dx2y + -4dy) = 0

Combine like terms: dx2y + dx2y = 2dx2y
2dx2y + -4dy = 0

Solving
2dx2y + -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), '2dy'.
2dy(x2 + -2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve:

Simplifying
dy = 0

Solving
dy = 0

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

Simplifying
dy = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(x2 + -2)' equal to zero and attempt to solve:

Simplifying
x2 + -2 = 0

Reorder the terms:
-2 + x2 = 0

Solving
-2 + x2 = 0

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

Add '2' to each side of the equation.
-2 + 2 + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + x2 = 0 + 2
x2 = 0 + 2

Combine like terms: 0 + 2 = 2
x2 = 2

Add '-1x2' to each side of the equation.
x2 + -1x2 = 2 + -1x2

Combine like terms: x2 + -1x2 = 0
0 = 2 + -1x2

Simplifying
0 = 2 + -1x2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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