In a national economy, I(t), Y(t) and C(t) denote (in trillions of dollars) the level of investment, income and consumption respectively at time t (in years) and these quantities are related by the equations C() = 1-Y'() and I1() = (1+3Y(t) – 4Y"() %3D with C(0) 1/2 and I(0) 7/2. If Y (t) = C(t) + I(t), show that Y(t) satisfies the differential equation Y"(t) +Y'(t) + and hence find Y (t). Deduce expressions for C(t) and I(t). Describe the behaviour of each of these three functions as t increases.
In a national economy, I(t), Y(t) and C(t) denote (in trillions of dollars) the level of investment, income and consumption respectively at time t (in years) and these quantities are related by the equations C() = 1-Y'() and I1() = (1+3Y(t) – 4Y"() %3D with C(0) 1/2 and I(0) 7/2. If Y (t) = C(t) + I(t), show that Y(t) satisfies the differential equation Y"(t) +Y'(t) + and hence find Y (t). Deduce expressions for C(t) and I(t). Describe the behaviour of each of these three functions as t increases.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:In a national economy, I(t), Y(t) and C(t) denote (in trillions of dollars) the level of
investment, income and consumption respectively at time t (in years) and these quantities
are related by the equations
C() = 1-Y'() and I1() = (1+3Y(t) – 4Y"()
%3D
with C(0) 1/2 and I(0) 7/2.
If Y (t) = C(t) + I(t), show that Y(t) satisfies the differential equation
Y"(t) +Y'(t) +
and hence find Y (t).
Deduce expressions for C(t) and I(t).
Describe the behaviour of each of these three functions as t increases.
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