TY - JOUR
AU - Tanner, H. W. Lloyd
AB - 1876.] 159 On the Bqucution dx dy dx dy By Prof. H . W . LLOYD TANNER, M.A. [Read January 11*A, 1877.] 1. The equation which forms the subject of this paper has not been discussed, as far as I know, except in the comparatively simple case in which P, Q do not involve the dependent variable z. An attempt is here made to supply this deficiency in part; viz., when the equation bas a general solution of a kind which may be described as follows :— I t expresses z in terms of two arbitrary functions <p (x), 4> (y). These arbitrary functions may occur under the sign of indefinite integration; but the only other quantity under the integrating symbol is the dif- ferential of the argument of the arbitrary function. Thus we may have n n | J ... <p (a>) dx , ff... \fj (y) dy [written $ (x) and 4> (y) in the sequel]; n n but not I [<p (a;)] dx. Many integrals not included in this definition are easily reduced to the form required. For instance, \x<f> (x) dx, which is a;^,—<f> . In Art. 13, below, another such integral occurs. Our problem 
TI - On the Equation d2zdxdy+Pdzdx+Qdzdy+Z=0
JF - Proceedings of the London Mathematical Society
DO - 10.1112/plms/s1-8.1.159
DA - 1876-11-01
UR - https://www.deepdyve.com/lp/wiley/on-the-equation-d2zdxdy-pdzdx-qdzdy-z-0-eL1lHnpGXh
SP - 159
EP - 174
VL - s1-8
IS - 1
DP - DeepDyve
ER -