Table 2.

Types of the ODE (9) depending on the given mortality.

Given mortality	Right-hand side of Equation (9)	Type of the ODE
m  and  m0	(1 − p){i − (m − m0)}	Linear
m  and  m1	(1 − p){i − p((m1 − m)/(1 − p))}	Linear
m 0  and  m1	(1 − p){i − p(m1 − m0)}	Riccati
m 0  and  R	(1 − p){i − pm0(R − 1)}	Riccati
m 1  and  R	(1 − p){i − pm1((R − 1)/R)}	Riccati
m  and  R	(1 − p){i − m((p(R − 1))/(p(R − 1)+1))}	Abelian