sicp exercise 3.78

;; Exercise 3.78. 



;;Figure 3.35:  Signal-flow diagram for the solution to a second-order linear differential equation.
;;Consider the problem of designing a signal-processing system to study the homogeneous second-order linear differential equation



;;The output stream, modeling y, is generated by a network that contains a loop. This is because the value of d2y/dt2 depends upon the values of y and dy/dt and both of these are determined by integrating d2y/dt2. The diagram we would like to encode is shown in figure 3.35. Write a procedure solve-2nd that takes as arguments the constants a, b, and dt and the initial values y0 and dy0 for y and dy/dt and generates the stream of successive values of y.


(define (display-line str)
  (display str)
  (newline))

(define (display-stream str num)
  (define (internal index)
    (if (> index num) 'printed
        (begin
          (display-line (stream-ref str index))
          (internal (+ 1 index)))))
  (newline)
  (internal 0))

(define (scale-stream stream factor)
  (stream-map (lambda (x) (* x factor)) stream))

(define (add-streams s1 s2)
  (stream-map + s1 s2))

(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-2nd a b dt y0 dy0)
  (define y (integral (delay dy) y0 dt))
  (define dy (integral (delay ddy) dy0 dt))
  (define ddy (add-streams (scale-stream dy a)
                           (scale-stream y b)))
  y)