Sol.4.2

# Sol.4.2 - 4.2 Exercises 1A-D C I B-n r0 A rn92 k'L | | f...

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Exercises 4.2 bf) B f 1 A A(-rnQ2 +A) +B(bO) :1 A (-DCI) * B (-nr0'+ A; : 3 rn92 - k (,,,(12-L-t2tli2()': \r,t\$! 'L | | v ), nr02 - A; t'os ( )f * (nr02 - k)' +b2Q2 b0 ',---1i rll : (nr02 - k)t +b292 (rn02 - k)'+b2Q2 I,b:0.1, arrd k:21t, the coeflicrielts A ancl B in part (a') a're {)2 - 2rt 0.102 A(o) : (sl, - 25)2 + o.o1 ' p/()\ - graplis of these functiotts ale sltorvu in Fig. 4-A : 7, b: 0, and k :25, the coefficients A and B A(o) : -"+, B(CI) , qraptrs of tliese functions are shown in Fig. 4 B' page 173' -. :0, then ecluation (7) reduces to rrt'y" * k:t1 : cos(-lf. : .' .titutin g 'A :,4 cos 9t + B sirr Ol vielcls nt (- Att2cosf)t - B1;zsinOl) + k (AcosOf * Bsi.Of) : cosOl + (-nt92 + k) (A cos Of * B sin Ot) : cos Ql ' ----'iptittg 1ow that 9: \EIn, we get -n't92 *A;:0' atid so the above ecluation - r:,possible rvith any c,hoice of A ancl B. .-'.rentiating y: (2nrO)-rlsinOt tu'ice, we obtain sin 01. (sz, - zs)2 + 0.01 ' on page 173. in part (a) becorne - 0. - =! (siu Q/ i /Q t',:s Q/1 . 2nr|l' u" : #r(2 cos 0t - tO sin 0l) 1A , u" + k!,t : t (2cos Ot - l0 sin Of) + ,,,,n, sin Ot : cos ar + ( -nr j-) 1j+q : ('os Qr . \ rrr{) ) '2 . -O + [email protected]): 0 if {l: \f|n. -:ES .1.2: Flornogeneous Linear Equations: The General Solution '--jiary eclutrtion, 12 +6r *9: (r+3)2 :0, 5as a double root r

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Chapter 4 a general solution is given by aQ):cte-3t+c2te-3t, where c1 and c2 a.re arbitrary constants.
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## This note was uploaded on 03/30/2009 for the course MA diff eq taught by Professor Fenn during the Spring '09 term at N.C. State.

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Sol.4.2 - 4.2 Exercises 1A-D C I B-n r0 A rn92 k'L | | f...

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