9. The diagram below shows a parcel, of mass \(m \mathrm {~kg}\), sliding down a rough slope inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = \frac { 7 } { 25 }\).
\includegraphics[max width=\textwidth, alt={}, center]{8f47b2ff-f954-42ec-8ecc-fc64313a7b89-24_394_906_497_584}
The coefficient of friction between the parcel and the slope is \(\frac { 1 } { 12 }\). In addition to friction, the parcel experiences a variable resistive force of \(m v \mathrm {~N}\), where \(v \mathrm {~ms} ^ { - 1 }\) is the velocity of the parcel at time \(t\) seconds.
- Show that the motion of the parcel satisfies the differential equation
$$5 \frac { \mathrm {~d} v } { \mathrm {~d} t } = g - 5 v$$
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