(x^2+2u)*du-2x*dx=0

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Solution for (x^2+2u)*du-2x*dx=0 equation: 


Simplifying
(x2 + 2u) * du + -2x * dx = 0

Reorder the terms:
(2u + x2) * du + -2x * dx = 0

Reorder the terms for easier multiplication:
du(2u + x2) + -2x * dx = 0
(2u * du + x2 * du) + -2x * dx = 0

Reorder the terms:
(dux2 + 2du2) + -2x * dx = 0
(dux2 + 2du2) + -2x * dx = 0

Multiply x * dx
dux2 + 2du2 + -2dx2 = 0

Solving
dux2 + 2du2 + -2dx2 = 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(ux2 + 2u2 + -2x2) = 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 '(ux2 + 2u2 + -2x2)' equal to zero and attempt to solve:

Simplifying
ux2 + 2u2 + -2x2 = 0

Solving
ux2 + 2u2 + -2x2 = 0

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

Add '-1ux2' to each side of the equation.
ux2 + 2u2 + -1ux2 + -2x2 = 0 + -1ux2

Reorder the terms:
ux2 + -1ux2 + 2u2 + -2x2 = 0 + -1ux2

Combine like terms: ux2 + -1ux2 = 0
0 + 2u2 + -2x2 = 0 + -1ux2
2u2 + -2x2 = 0 + -1ux2
Remove the zero:
2u2 + -2x2 = -1ux2

Add '-2u2' to each side of the equation.
2u2 + -2u2 + -2x2 = -1ux2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
0 + -2x2 = -1ux2 + -2u2
-2x2 = -1ux2 + -2u2

Add '2x2' to each side of the equation.
-2x2 + 2x2 = -1ux2 + -2u2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
0 = -1ux2 + -2u2 + 2x2

Simplifying
0 = -1ux2 + -2u2 + 2x2

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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