The derivation of the differential equation for p in the text requires combining two differential equations for a and b. Often, one can find a differential equation for a new variable derived from a single equation. In the above cases, use the chain rule to derive a new differential equation.
Suppose dx/dt = 2x - 1. Set y = 2x - 1 and find a differential equation for y. The end result should be simpler than the original equation.