MATH 202 Exam 2 with Solution, Fall 1998

Prof. N. Haidar FACULTY OF ARTS & SCIENCES , A. U. B. Sec. 1&2 Math 202 6 Jan.,1999 (1-st Semester , 1998-1999) : Time : 1 hour Quiz , , (closed book) @ I) Solve the BVP a yoty =x +1 3 y(O)=s, y=0. @ Il. Solve the IVP vy + xy-y=4x 3) y(i)= y¥(1)=0. @ III. Find the general power series solution of the following DE about the ordinary point x =0. (7-1) y” taxyt2y =0. @ IV. Apply the method of Frobenius to find one of the solutions to the DE (x-l)y" +y = 0, in the neighborhood of its x = | singularity . 1 ~ ar % . 4 Wis |< aan - at ( { -% =a —>* a-txte lk a n ! w= |o 5 ; as l 2e-t ‘ a yt xt? Qo xe = w Wr il* L a =4 » ais We 2 4 > w - “ie eee NOD _~ 4 ul . 7 ~! Y ae t4n = Cee er_xtax%e —% u _ ) <_D Yu Cie a Ca xT tx Ar | ; JQ) = Cteyno =_ Yu eer CK + zkux+ 2 dooee HED 2¢, +t =o Gz DE) Cr21-C, = | . Sox see ex . _ 3 + + 2% nse > |O av 2B “4 / Oe ay + txy +249 20 @ =_ u / = ~ Y= 2Q4U 2 ely yyt! 4 >) - wee ? J Ros ‘ * ag = Z tlr-1) C, >" é oo _ - 4=¢ 2 . — u-t md EN) ZAC x ey Sad yl at C Hee ho re 2. “= O “~ a ~< t-2 ba) a ST nina _ AH-X A g S , a t 2. pte Ge =* ) on 4 Zr +2 26, ~*~ > 6 en _~ 4 = de ® we ania ; > ZHENG Ley ae De riety Ga y2e _ | = ~ SES — te <— —_ Dut) C, WX 2uti er) Gap eee gy axe up 2S Qe = & mee Kos Koo Wags “3 > Fe" Sulu) Gy —Cete er) tz boa Ce £2 CQ. t =o Nua & FE ¢* § Cu [utient) #4 FUT —Gere yer) ez \ = 0 wt take = etete er? = Ce r2)CK+!) =e Cu CutiCu rt) -CereayCer) Ge+r ee 2s | Gace = 2. | We ceurience. litn . K=O 3 Cyr se Qe wo{ : Cz = @, C, #o w=2 Cee Ce eho WK=y sa C3 Kaqs Ce Cys Cree wae Cpe Cea C3 2h —_— aut! Jz Q Be 4+ GUD @) woe mre \ J,G@) = 2 eZ Tel re (iso! | \L