Question

x'-y,y 10x-7y using the method of elimination. 2) a) Find the general solution to b) What happens to all solutions as ? You should find that all solutions approach the same point (x, y). This is an example of a fixed point. c) Find the particular solution to the IVP consisting of the above system of equations and the conditions x(0)2, y(0)-7

Answer 1

a) here d2 2 w. e.t t diereanfate equaton lox R-Ra-- + De d 2 D lo oguation 2 mt7m +10 0 m2+ 2m+ Smn+lo o + s (m+2)o m(m+2) Cm+ 2) (m+s) mz-2, - S st -2t t) Cie

put the valu st 7C2e -24 - 20e 7C16 (0x -3t +2 e lo x -2 CIe -St + e 2 Soluhions 2t are e st J 2 - 4 e e Jt as t a alu doluton a'prohes the (0,0) point dame hen. are

c) -5t = (t)X 2t Ge x (o) 2 , IVP put in Aystem doluton the nlo) 2 SC + 202 10 7o-7 3Y 5+202= 10 Ci 4-7 and dutac equahsn mu SC + 2C2= 1o 2C, 2= -14 3C + o CE8 put in 4 8+ 1 -7 S1-37 jut vale CI and c in the dolut.n then n(t) and d becomes 2t 3e-St (t)= 4e - -5t 15 e Be
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