Exercise 3.78: Consider the problem of designing
a signal-processing system to study the homogeneous second-order linear
differential equation
d
2
y
d
t
2
−
a
d
y
d
t
−
b
y
=
0.
The output stream, modeling y, is generated by a network that contains a
loop. This is because the value of d
2
y
/
d
t
2 depends upon the
values of y and d
y
/
d
t and both of these are determined by
integrating d
2
y
/
d
t
2. 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 d
t and the initial values
y
0 and d
y
0 for y and d
y
/
d
t and generates the
stream of successive values of y.
SVG
Figure 3.35: Signal-flow diagram for the solution to a second-order linear differential equation.
练习 3.78：考虑设计一个信号处理系统来研究齐次二阶线性微分方程 d²y/dt² − a(dy/dt) − by = 0。对 y 建模的输出流由一个含有回路的网络生成，这是因为 d²y/dt² 的值依赖于 y 和 dy/dt 的值，而这两者都是通过对 d²y/dt² 进行积分来确定的。我们希望编码的图示如图 3.35 所示。请写一个过程 solve-2nd，它以常数 a、b、dt 以及 y 和 dy/dt 的初始值 y₀ 和 dy₀ 为参数，生成 y 的连续值的流。
SVG
图 3.35：二阶线性微分方程解的信号流图。