Variation Problems for a Symmetrical Region

IF, in Prof. Bateman's example, we take then φ and ψ may be regarded as independent of each other, and the variational equations are It is true that the equation can be derived by adding these two equations, but it represents only a part of the variational system: the whole set consists of the above two equations, which when we eliminate ψ give and I regard this as the true differential equation arising in Prof. Bateman's problem.