Your answer with part a of multiplicity three with

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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....
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