106 Mr murphy, on THE RESOLUTION OF EQUATIONS, &c. 



which sohition is particular, since it contains only one arbitrary constant, 

 viz., y'(0) or 7; denote this value of u, by JT,, and put u,= X^ + c,, 

 and having found v^ with another arbitrary, from the transformed equa- 

 tion, put y,, = JC-i + t,, X-i containing two arbitraries, and by continuing 

 this process, we shall obtain the complete solution, viz., 



«., = X, + X + X + + X,. 



R. MURPHY. 



Caius College, 

 'Nov. \, 1835. 



