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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

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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