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sicp-all-tasks/sicp/3_002e78

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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
.