Your answer with part a of multiplicity three with

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: has one eigenvalue, (a) compare .your answer with part (a). , of multiplicity three with one Show 0 x < 0. (b) linearly independent eigenvector,x), y2 (x)Ay find (one solution of the Use general solution of the y1 ( v1 y = are linearly dependent on definition show that 6. Find thethe definition show that systemy.2 (Hence linearly where (c) Use the y 1 ( x) , x) are + F x) independent on system. x < 0. IR. 21 4xe x (b) Find two more independent solutions) ) described . A= (c) Use the definition show that ,yand ,F(xxasare linearly in class. Verify ( x) y 2 ( = independent on 1 2 (d) Show that W (y1 (x), y2 (x)) = 1 for all x IR. 0 0 that IR. the three solutions are linearly independent. Hence give the 7. Consider a solution of )withxconstant supply SIR. 50 and demand curve = (d) general commodity the2system.0 for all x Show that W (y1 (x , y ( )) = whose derivative is given by dD = 2D 5p + 10 dt where D is the demand and p is the price. The rate of increase of the price is 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....
View Full Document

Ask a homework question - tutors are online