l 35 ] 



V. On the Solution of Linear Partial Differential Equations of 

 the Second Order involving two Independent Variables. By 

 R. Moon, M.A., Honorary Fellow of Queen's College, Cam- 

 bridge*. 



THE following method of treating the problem offered to us 

 in the solution of the General Linear Partial Differential 

 Equation of the Second Order, in the cases which are not amen- 

 able to Mongers method, may be found to possess both interest 

 and value. 

 Let 



°= r S +s ^ +t S +p £ +q I +u ^ v ' • (1) 



where R, S,T,P,Q,U, V are functions of x and y only; and assume 

 *= A + A4>{u) +A l ^- 1 (u) +A 2 </>- 2 (w) + R, &c, . (2) 

 where u, A, A, A v A 2 , &c. are functions of x and y only, and 



$-*{u)=ff${u)du\ 



&c. &c. 



Our assumption gives us 



dz _ dA i\du t( . 

 dx~~ dx dx ^ v ' 



du dA\ , i x f k du dA, 



+ 



(A.J + ^W+C^E + ^-W^ 



dz dA K du ,,, . 

 Ty=dy +A ^ u) 



^K^>H^t>^ )+kc - 



cPz d*A , du\ q ,.., , 





+ ( A -1 



3 2 dA^du d% d 2 A/ 

 dx dx 2 dx 2 dx 2 , 



+ &C. 



* Commu 



nicated by the Author. 

 D2 



)+-'(«) 



