Unformatted text preview: is the demand and p p is the price. The rate increase of the the is
price is the rate of decrease of the quantity.
equal to equal to the rate of decrease of the quantity.
(a) Write down a system of di erential equations for D(t) and p(t) that
models the situation described above.
(b) Find the equilibrium solutions of the system, if any.
(c) Find the general solution of the system.
* You may use Maple to help you with the following two problems. If you
do, include a printout of your worksheet(s) with your assignment.
8. Consider the system y = Ay, where
A= 421
043
004 . (a) Show that A has one eigenvalue, , of multiplicity three with one
linearly independent eigenvector, v1 . Hence ﬁnd one solution of the AMATH 350 Page 2 Assignment #7  Fall 2012 5. Solve the following boundary value problem.
ux y u = xey , u(1, y ) = cos(y ) 6. Consider the PDE
uyy (2) (3) 4u = sin (xy ) . This can be solved by using our knowledge of second order ODEs, as follows:
a) Find the solution uh (x, y ) of the associated homogeneous equation uyy
4u = 0 (the arbitrary constants will bec...
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 Fall '12
 DavidHamsworth
 Boundary value problem, general solution

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