(v^2)dx+[x(x+v)]dv=0

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Solution for (v^2)dx+[x(x+v)]dv=0 equation: 


Simplifying
(v2) * dx + [x(x + v)] * dv = 0

Multiply v2 * dx
dv2x + [x(x + v)] * dv = 0

Reorder the terms:
dv2x + [x(v + x)] * dv = 0
dv2x + [(v * x + x * x)] * dv = 0
dv2x + [(vx + x2)] * dv = 0

Reorder the terms for easier multiplication:
dv2x + dv[vx + x2] = 0
dv2x + [vx * dv + x2 * dv] = 0

Reorder the terms:
dv2x + [dvx2 + dv2x] = 0
dv2x + [dvx2 + dv2x] = 0

Reorder the terms:
dvx2 + dv2x + dv2x = 0

Combine like terms: dv2x + dv2x = 2dv2x
dvx2 + 2dv2x = 0

Solving
dvx2 + 2dv2x = 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), 'dvx'.
dvx(x + 2v) = 0


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

Simplifying
dvx = 0

Solving
dvx = 0

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

Simplifying
dvx = 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 '(x + 2v)' equal to zero and attempt to solve:

Simplifying
x + 2v = 0

Reorder the terms:
2v + x = 0

Solving
2v + x = 0

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

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

Combine like terms: 2v + -2v = 0
0 + x = 0 + -2v
x = 0 + -2v
Remove the zero:
x = -2v

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

Combine like terms: x + -1x = 0
0 = -2v + -1x

Simplifying
0 = -2v + -1x

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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