sicp exercise 3.79

;; Exercise 3.79.  Generalize the solve-2nd procedure of exercise 3.78 so that it can be used to solve general second-order differential equations d2 y/dt2 = f(dy/dt, y).

(define (integral delayed-integrand initial-value dt)
  (define int
    (cons-stream initial-value
                 (let ((integrand (force delayed-integrand)))
                   (add-streams (scale-stream integrand dt)
                                int))))
  int)

(define (solve f y0 dy0 dt)
  (define y (integral (delay dy) y0 dt))
  (define dy (integral (delay ddy) dy0 dt))
  (define ddy (stream-map f y dy))
  y)