MATH 202 Exam 2 with Solution, Fall 1997

Prof. N. Haidar FACULTY OF ARTS & SCIENCES , A. U. B. Sec. 1&2 Math 202 19 Jan., 1998 (1-st Semester , 1997-1998) Time: [ hour QUIZ I (closed book) @ 3. Solve the [VP yy ry + yr By =O 2) y= 0, yo) = 2, y" (0) 5-12, ® UW. Find the general solution of the DE 7] 2 y + y = csecx +X © UL Apply the method of Frobenius to find the general solution of the DE x(l-x)y” - 3¥ +2y = 0, in the neighborhood of its x = 1 singularity . ® IV. Use the substitution y = vx u(x) to reduce the DE y'+[e? - k(e-l)/ x) y=0;keEN,c>0, to an equivalent Bessel’s DE, then express its solution in terms of Bessel functions . a). . at w/a / cnc eensin ne i) TVG: ERY FY + 1792 0, Iolaa yore 2, Ter2 -12 7 me +6m+ 13 ig. mM Bie -+ gacrl3 = oO Ge) . watt Tm + Fm 419m FZ (mt On} 6m +13) =o) 7 ae 6 nft + igm th . ~€yxt Fem | ! ~ ’ 9-14 =-3AtL . aed us -3t -3I9C . “(es Cro 2x + C3 &nt*) CL) Gio) Ce -3Ot e224 =F a Q ) peo nee Hed $24 Ce ) , 5* -3 LX) A J @,c +9 Centar -3% clot ¥— 43 Sc 1%) ae 42egcat®™)t © Gc Co = 12 a 3 “Gnesi 2 Ge) 3O = — ree ! woo. © uA ye a y + Zgexy J =v >— _ _97y kb 2y 2s - ie xU-xd Y- 29 y =) =x) . ay ay it —_ ds ‘ wa ° oD ead » x = {-t > ay = ee dt 3 y= J \ + 3uy + a y= ‘Oo , ve es) £U-t) eci-é) ———— r=0O = “4 pe : Tf =3 Pad, VR2 ro) ,Pe 3p eee = grate re ee } - )= 7 re na 4 2.23 7, =0 ya 2 007! CH) ,= Qe 2 = 3D at a eek +26 a "Ye ¥ 2. Car) t i-t hi0 ¥, = 7 L Y-va = = Ke} a! 4. >| | _ et. 3 ley’ Berths = ner -2) ga 4 7 _ { —Y he = 7 q be (nn -l [- the _ b, J =e =) 2(2-t) oo ‘i -~ yp t2, byt nucv 2| ; | CLahe - tibedy 27 yee : —_—_— - ° . ' _ G-t) aye 2 . ye ea bes bi vabe +53) 6 . gat) wi, es bs t8 by) _ ) . Oo 4 \-4hu- 7 oe . - ey arn : =O. von bz= 7 “4. a 2 ht. ptbat 4+:t [ bet an) o 1 a at Fat in ale Ceh wleM/e JS =O ye eo Ww y= a ~ J 2 ; ° ys Lat U+ aot wb a) | _ tc mae Dortul +r’ @) yi et aot u + + a LL +2 = 4 if -4 ui-t wt ane ; ») =u i) -i — At CK at _ pow ke GU *UFLE we ”'> tO +u ry, oF “ae ot eee Tu = 8 u + 7 L aS L te uua | _ Lot ele!) - & Ws o tet - O Z ip ok ia ta ul pct! + | x -«& +) ; - "ok ~-ces 24 UL us Jaks dt | eer . ; ix 3 : - Ee uz of Ww _ ef d 4 v [e- aut ee t ue) = 1 j,.@ +8 Ji) as ee) oa) OL SY . 1