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 = x + x2. Set y = 1/x and find a differential equation for y. This transformation changes a nonlinear differential equation for x into a linear differential equation for y (this is called a Bernoulli differential equation).