m s Equation m s Equation

24. yy′x = y + f (x). Abel equation (Abel differential equation) of the second kind in the canonical form. 1. Solvable Abel equations. Tables 1–4 list all the Abel equations whose solutions are outlined in Handbook of Exact Solutions for Ordinary Differential Equations by Polyanin & Zaitsev. Tables 1–3 classify Abel equations in which the functions f are of the same form; Table 4 gives other Abel equations. In Table 1, equations are arranged in accordance with the growth of the parameter m. In Table 2, equations are arranged in accordance with the growth of the parameter p. In Table 3, equations are arranged in accordance with the growth of the parameter s. The rightmost column of the tables indicates the equation numbers where the corresponding solutions are written out. TABLE 1 Solvable Abel equations of the form yy′x − y = sx + Axm, A is an arbitrary paramete