v^2dx+x(x+xv)dv=0

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


Simplifying
v2dx + x(x + xv) * dv = 0

Reorder the terms:
dv2x + x(vx + x) * dv = 0

Reorder the terms for easier multiplication:
dv2x + x * dv(vx + x) = 0

Multiply x * dv
dv2x + dvx(vx + x) = 0
dv2x + (vx * dvx + x * dvx) = 0

Reorder the terms:
dv2x + (dvx2 + dv2x2) = 0
dv2x + (dvx2 + dv2x2) = 0

Reorder the terms:
dvx2 + dv2x + dv2x2 = 0

Solving
dvx2 + dv2x + dv2x2 = 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 + v + vx) = 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 + v + vx)' equal to zero and attempt to solve: Simplifying x + v + vx = 0 Reorder the terms: v + vx + x = 0 Solving v + vx + x = 0 Move all terms containing d to the left, all other terms to the right. Add '-1v' to each side of the equation. v + vx + -1v + x = 0 + -1v Reorder the terms: v + -1v + vx + x = 0 + -1v Combine like terms: v + -1v = 0 0 + vx + x = 0 + -1v vx + x = 0 + -1v Remove the zero: vx + x = -1v Add '-1vx' to each side of the equation. vx + -1vx + x = -1v + -1vx Combine like terms: vx + -1vx = 0 0 + x = -1v + -1vx x = -1v + -1vx Add '-1x' to each side of the equation. x + -1x = -1v + -1vx + -1x Combine like terms: x + -1x = 0 0 = -1v + -1vx + -1x Simplifying 0 = -1v + -1vx + -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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