int(5v-u)du+(3v-7u)dv=0

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Solution for int(5v-u)du+(3v-7u)dv=0 equation: 


Simplifying
int(5v + -1u) * du + (3v + -7u) * dv = 0

Reorder the terms:
int(-1u + 5v) * du + (3v + -7u) * dv = 0

Reorder the terms for easier multiplication:
int * du(-1u + 5v) + (3v + -7u) * dv = 0

Multiply int * du
dintu(-1u + 5v) + (3v + -7u) * dv = 0
(-1u * dintu + 5v * dintu) + (3v + -7u) * dv = 0

Reorder the terms:
(5dintuv + -1dintu2) + (3v + -7u) * dv = 0
(5dintuv + -1dintu2) + (3v + -7u) * dv = 0

Reorder the terms:
5dintuv + -1dintu2 + (-7u + 3v) * dv = 0

Reorder the terms for easier multiplication:
5dintuv + -1dintu2 + dv(-7u + 3v) = 0
5dintuv + -1dintu2 + (-7u * dv + 3v * dv) = 0
5dintuv + -1dintu2 + (-7duv + 3dv2) = 0

Solving
5dintuv + -1dintu2 + -7duv + 3dv2 = 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(5intuv + -1intu2 + -7uv + 3v2) = 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 '(5intuv + -1intu2 + -7uv + 3v2)' equal to zero and attempt to solve:

Simplifying
5intuv + -1intu2 + -7uv + 3v2 = 0

Solving
5intuv + -1intu2 + -7uv + 3v2 = 0

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

Add '-5intuv' to each side of the equation.
5intuv + -1intu2 + -7uv + -5intuv + 3v2 = 0 + -5intuv

Reorder the terms:
5intuv + -5intuv + -1intu2 + -7uv + 3v2 = 0 + -5intuv

Combine like terms: 5intuv + -5intuv = 0
0 + -1intu2 + -7uv + 3v2 = 0 + -5intuv
-1intu2 + -7uv + 3v2 = 0 + -5intuv
Remove the zero:
-1intu2 + -7uv + 3v2 = -5intuv

Add 'intu2' to each side of the equation.
-1intu2 + -7uv + intu2 + 3v2 = -5intuv + intu2

Reorder the terms:
-1intu2 + intu2 + -7uv + 3v2 = -5intuv + intu2

Combine like terms: -1intu2 + intu2 = 0
0 + -7uv + 3v2 = -5intuv + intu2
-7uv + 3v2 = -5intuv + intu2

Add '7uv' to each side of the equation.
-7uv + 7uv + 3v2 = -5intuv + intu2 + 7uv

Combine like terms: -7uv + 7uv = 0
0 + 3v2 = -5intuv + intu2 + 7uv
3v2 = -5intuv + intu2 + 7uv

Add '-3v2' to each side of the equation.
3v2 + -3v2 = -5intuv + intu2 + 7uv + -3v2

Combine like terms: 3v2 + -3v2 = 0
0 = -5intuv + intu2 + 7uv + -3v2

Simplifying
0 = -5intuv + intu2 + 7uv + -3v2

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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