Systems of First-Order Equations

Systems of differential equations arise very naturally in many physical contexts. If y1, y2, . . . , yn are functions of the variable x, then a system, for us, will have the form

y′1 = f1(x, y1, . . . , yn) y′2 = f2(x, y1, . . . , yn)

. . . y′n = fn(x, y1, . . . , yn) .