l8o MATHEMATICAL FORMULA AND ELLIPTIC FUNCTIONS 



8.404 Resolution of the operator. The differential equation: 



d 2 y dy 



u ^ + v-f L + wy = o, 

 dx 2 dx 



may sometimes be solved by resolving the operator, 



d 2 d 



into the product, 



The solution of the differential equation reduces to the solution of 



The equations for determining p, r, q, s are: 



ds 



8.410 Variation of parameters. The complete solution of the differential 

 equation: 



s 



y = cJ t (x)+oj l (x)+ 



where f\(x) and f 2 (x) are two particular solutions of the differential equation 

 with R = o, and are therefore connected by the relation 



C is an absolute constant depending upon the forms of /i and fz and may be 

 taken as unity. 



8.500 The differential equation: 



(#2 + b^x) ~j$ + (#1 ~\- biX) ~ h (#0 + 



8.501 Let 



D = (dobi d]bo 



