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# N0905 - ME 3‘“ 0‘1 tan/QQ ﬁg CLASS NOTES[5514,92 We...

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Unformatted text preview: / ME 3‘“ 0‘1 tan/QQ _, ﬁg; CLASS NOTES [5514,92 We «VA/\faq 97! {1‘42 LN‘K 97.7. '5) 0th: ~am 37L AJC 91—,Rj an? d _ GM (MCFSW) TUL =J GM:+§R :1 “av 313.7“ 917. Q14: W V1491 WC 017E “1 an index Vow 0“ n M” of; 13: 91 Z. ’L A+ hLKJ VLVO :) v11” yﬂL—I—C L — Tr) C=ch__ K : 9K LOB/l 5) v2 ,zﬁf +23} ,(72 2. 71 l V 7900 l l 0 ~ 0 +Vo . ._(7K LOB/2. Luz/j CHAPTER 2 : FIRST — ORDER DIFFERENTIAL EQUATIONS 2.3 Linear Equations Standard Form: dy/dx + P(x) y = f(x) Solution Method: Integrating Factor approach 1. Find Integrating Factor (IF) 2. Multiply equation by IF. and integrate both sides EN? W oh‘ffwuﬂ 52%” be,“ a. x) al A C (11% Meow/Vim) ,0) fo’vwx ‘ a +PCX)\ , W /~ >0 «2) Assam y 5 UL 6 Sum 07L +00% ytyc+yp (mow/\Q >IC {5 a Jae-«WM 075 M anaemia; QW2m 51‘an QWFo-vx (3) Q vm‘oA/QQ &PM,UULQ Can #MyCLOZ/L' -——+ y ,9 031; ,PijoLx J 2v” {Pawn +£«q _ PC) yZCQ/ you '5le Va’ua/Efm O'F gash {Ana 0 t: bk Jack M ypl y) CK) 1} Ct 36W 07L Subs/Uh;th Y? I?“ (2) W PM 74M % L4. (Nat W H>ﬂc+79 3W7 MW) .3 PCXJOK ) Q; x7 ; C+/Q/PLX)OLX fax) o/Lx DiffM/h‘ahz [Pen cu [PQ‘JoLX \ 0L (2, : C IKE }] 2 2C X) ijuuotx , + PM) QfPLxJOuy : QfPijoquX/ Pm .‘ a}: + may 2 foj on LOB/5 I": : QfPC/(Jckx 2~ W9} :‘F jpmokxok fPCXQoLx [pend Q .Q_ : X 9% + j 2 f—Cx/ hwy LHJ‘ 03 CL fﬂHoLx ' f/ch) okx l; [a y] _ Q by f? CX) Ax /? Ci) at; :9 Q )1: C+/JL )CCXJOlX _ [Pmdx -chxJOLx PC 294 m j : CQ + \$2 2/ X K/ijAx EM“ x a: +Zu >Sx AK 0le Q. (L z 5 11* 3? 2 ﬂow a % 1+:fo if” a: « 2h)“ “LACIE ; M30” {QAsz : mer" 3 I~F 3K1 '2 x N 0L“: 2M 2 QCS” C 0M+ ,x— j Y J XrLU.‘ 5L}.+ C 3 : U:Sx S. J 3+ x1 WNW. at: :5 — 3.9 w okx 3 x3 1 L‘H'5,% S 2,; ,Sx‘_2_g_ Z 535+£ 3 7(3), ’3— 7g 1 [3 X1] 42. \4 X 3 5X1, 6. +‘f_’_2<1+ ’3 x 3 K .1sz 2344‘; EXawVp/Qe 2._. F4224»? bud), “MM Gun. msljiamca bV 5—34 0 caeHw‘ w m) “i 0 Am d“? «Anion? LOB/6 pvt hf 2'“ v — g; .2“ 4 c b .3f 0" V: C9. + “:2 b T a C=Vo’“i ‘9 2+ '9 V: (0*MJ)Q'M *3}: T b “2* _:+ V67): \IOCL M+(\—Q.M)\N_:cz b h£ L 03/7 L02 /3 2.3 Exact Equations Definition: A first order differential equation of the form M(x,y)dx+N(x,y)dy=0 is an exact differential equation if the expression M(x,y)dx+N(x,y)dy is an exact differential of a function f(x). Theorem: A necessary and sufficient condition that M(x,y)dx+N(x,y)dy be an exact differential is zigzag 3y ax Spaqi-CL C952 2 x 3‘3 +51 0Ler Li Xyzc xd/‘qyotx .3 0w. J;an ou‘f/WJGQQ o7C y 0+7; like QCvxr-eJGom Y dy+y&¥:o i) an QAKGU“ W041 Gm: La 2.; KW JZ:CL£OLX+ Qid ex A), J «H ()y TR») MW ‘27 {Cw/kc ,wkdk 52% W sea/WM *6 ~ Lo (WM MCX,y)oL><+ NijyJolj :0 ~69 3/? 1% Mex, )zcﬁ W ch,):# W \m‘ y &X j J}— ./ (2W .3 Qxaut. W’tu W 73 g 0,)(fjﬁ 4 7€A 3y ax MGR 91E: MLY/y) M £;Ncéyj a« 6} O '9 I 7 ~ "' P3 I \ Gel L ) ‘ ‘ C¥j % £24K ‘ swing/"hm w Cit-HM“ 29'.) v PJWGM W C ‘ am, :wa) ﬁlly) LC .3 a ram 01" We give)“ Eﬂouwp/qe : =) 7L;>(j+y " o‘ll -\—p\e 0L2. a xy+y :Q \5 a S‘dQui-D’K ...
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N0905 - ME 3‘“ 0‘1 tan/QQ ﬁg CLASS NOTES[5514,92 We...

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