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AMath350.F12.A7

# The rate increase of the the is price is the rate of

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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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