(1+U^2)DV=(1+V^2)DU

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Solution for (1+U^2)DV=(1+V^2)DU equation: 


Simplifying
(1 + U2) * DV = (1 + V2) * DU

Reorder the terms for easier multiplication:
DV(1 + U2) = (1 + V2) * DU
(1 * DV + U2 * DV) = (1 + V2) * DU

Reorder the terms:
(DU2V + 1DV) = (1 + V2) * DU
(DU2V + 1DV) = (1 + V2) * DU

Reorder the terms for easier multiplication:
DU2V + 1DV = DU(1 + V2)
DU2V + 1DV = (1 * DU + V2 * DU)
DU2V + 1DV = (1DU + DUV2)

Solving
DU2V + 1DV = 1DU + DUV2

Solving for variable 'D'.

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

Add '-1DU' to each side of the equation.
DU2V + -1DU + 1DV = 1DU + -1DU + DUV2

Reorder the terms:
-1DU + DU2V + 1DV = 1DU + -1DU + DUV2

Combine like terms: 1DU + -1DU = 0
-1DU + DU2V + 1DV = 0 + DUV2
-1DU + DU2V + 1DV = DUV2

Add '-1DUV2' to each side of the equation.
-1DU + DU2V + -1DUV2 + 1DV = DUV2 + -1DUV2

Reorder the terms:
-1DU + -1DUV2 + DU2V + 1DV = DUV2 + -1DUV2

Combine like terms: DUV2 + -1DUV2 = 0
-1DU + -1DUV2 + DU2V + 1DV = 0

Factor out the Greatest Common Factor (GCF), 'D'.
D(-1U + -1UV2 + U2V + V) = 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 '(-1U + -1UV2 + U2V + V)' equal to zero and attempt to solve:

Simplifying
-1U + -1UV2 + U2V + V = 0

Solving
-1U + -1UV2 + U2V + V = 0

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

Add 'U' to each side of the equation.
-1U + -1UV2 + U2V + U + V = 0 + U

Reorder the terms:
-1U + U + -1UV2 + U2V + V = 0 + U

Combine like terms: -1U + U = 0
0 + -1UV2 + U2V + V = 0 + U
-1UV2 + U2V + V = 0 + U
Remove the zero:
-1UV2 + U2V + V = U

Add 'UV2' to each side of the equation.
-1UV2 + U2V + UV2 + V = U + UV2

Reorder the terms:
-1UV2 + UV2 + U2V + V = U + UV2

Combine like terms: -1UV2 + UV2 = 0
0 + U2V + V = U + UV2
U2V + V = U + UV2

Add '-1U2V' to each side of the equation.
U2V + -1U2V + V = U + UV2 + -1U2V

Combine like terms: U2V + -1U2V = 0
0 + V = U + UV2 + -1U2V
V = U + UV2 + -1U2V

Add '-1V' to each side of the equation.
V + -1V = U + UV2 + -1U2V + -1V

Combine like terms: V + -1V = 0
0 = U + UV2 + -1U2V + -1V

Simplifying
0 = U + UV2 + -1U2V + -1V

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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