ON THE MANNER 



IN WHICH 



ALGEBRAIC FUJYCTIOJVS 



OF THE PRINCffAL VARIABLE, 



ARE IN CERTAIN CASES 



INTRODUCED INTO THE INTEGRALS 



OF 



LINEAR DIFFERENTIAL EQUATIONS 



THAT HAVE CONSTANT COEFFICIENTS. 



BY THE REV. EDWARD HINCKS, A.M. F.T.C.D. M.R.I.A. 



Read 16th March, 181S. 



LET F = o ; r being a linear function of <p.j, -^-^, -^> 



^^^^, and <p.^ being an unknown function of x, which it is the 

 business of the integration to determine. This function is in its 

 nature an exponential one. For, let a be any root of the equation 



V = o; V being what V becomes, when the exponent of the cha- 

 racteristic d of each term is transported to the right of the suffixed 

 VOL. XIII. R 



