OFind the general solution to the following third-order differential equa- tion + 2y = 3e using the method of undetermined coefficients. O Company A has a pricing policy that they need to follow in order to set price of good P(t), based on the forecasting sales S(t), inventory level L(t), production level Q(t) and and optimum level Lo (Lo is a constant value). There are various models for pricing policy that the company need to refer on the good produced. One of the models is dP -k(L(t) – Lo), dt TP Q(t) – S(t), dt dP dt S(t) = 100 – 52P Q(t) = 18 – 4P, where k is a constant value.
OFind the general solution to the following third-order differential equa- tion + 2y = 3e using the method of undetermined coefficients. O Company A has a pricing policy that they need to follow in order to set price of good P(t), based on the forecasting sales S(t), inventory level L(t), production level Q(t) and and optimum level Lo (Lo is a constant value). There are various models for pricing policy that the company need to refer on the good produced. One of the models is dP -k(L(t) – Lo), dt TP Q(t) – S(t), dt dP dt S(t) = 100 – 52P Q(t) = 18 – 4P, where k is a constant value.
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:a) Find the general solution to the following third-order differential equa-
tion
+ 2y = 3e
using the method of undetermined coefficients.
b) Company A has a pricing policy that they need to follow in order to set
price of good P(t), based on the forecasting sales S(t), inventory level
L(t), production level Q(t) and and optimum level Lo (Lo is a constant
value). There are various models for pricing policy that the company
need to refer on the good produced. One of the models is
dP
- -k(L(t) – Lo),
dt
TP
Q(t) – S(t),
dt
dP
S(t) = 100 – 52P – 14
dt
%3D
Q(t) = 18 – 4P,
where k is a constant value.
i. Show that the model can be presented as a second order differential
equation
dP
dP
+ 14k
+ 48KP = 82k.
dt?
dt
ii. Solve the second order differential equation in (i) by using the method
of variation of parameters if k = 1.
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