4 A particle of mass \(m \mathrm {~kg}\) is released from rest at a fixed point \(O\) and falls vertically. The particle is subject to an upward resisting force of magnitude \(0.49 m v \mathrm {~N}\) where \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) is the velocity of the particle when it has fallen a distance of \(x \mathrm {~m}\) from \(O\).

1. Write down a differential equation for the motion of the particle, and show that the equation can be written as \(\left( \frac { 20 } { 20 - v } - 1 \right) \frac { \mathrm { d } v } { \mathrm {~d} x } = 0.49\).
2. Hence find an expression for \(x\) in terms of \(v\).