Find the differential equation representing the family of curves ν = Ar + B, where A and B are arbitrary constants.

Given family of curves is v = Ar + B. Differentiating once, we get: dv/dr = -Ar⁻². ⇒ r² dv/dr = -A Differentiating once more, we get: d²v/dr² = 2Ar⁻³ r² d²v/dr² + 2r dv/dr = 0. This is the required differential equation representing the given family of curves.