... boundaryconditionsat bothendpointsare ultimately satisfied. At x 1 , the solution is supposed to satisfyB1j(x 1 ,y 1 ,y2, ,yN)=0 j =1, ,n 1 (17 .0.2)while at x2, it is supposed to satisfyB2k(x2,y 1 ,y2, ... equations,satisfying n 1 boundary conditions at the starting point x 1 , and a remaining set ofn2= N − n 1 boundary conditions at the final point x2. (Recall that all differentialequations ... the system (17 .0 .1) has a solution satisfying a total of N +1 boundary conditions. Here we again add an extra constant dependent variable:yN +1 ≡ x2− x 1 (17 .0.7)dyN +1 dx=0 (17 .0.8)We also...