Proceedings of the Edinburgh Mathematical Society

Table of Contents - Volume 5 - 1886  

Research Article

On a Differential Equation and the Construction of Milner's Lamp

Professor Cayley

What sort of an equation is

S0013091500001504_eqn1

Write

S0013091500001504_eqn2

and start with the equations

S0013091500001504_eqn3

This last gives

S0013091500001504_eqn4

and the system thus is

S0013091500001504_eqn5

viz., this is a system of ordinary differential equations between the five variables θ, r, X, Y, Z: the system can therefore be integrated with 4 arbitrary constants, and these may be so determined that for the value β of θ, X, Y, Z shall be each = 0; and r shall have the value r0.