MATH 202 Exam 1, Fall 2017

Notes before solving the exam: 1) You have to solve the recommended problems in the book after understand- ing each chapter from the book and the notes. 2) Please understand that this exam is solved by students, and it may contain Math 202 - Quiz 1 (Fall 17) some mistakes. T. Tlas 3) If you have any questions or con- cerns, let us know through our mail: in- sightclub@gmail.com. GOOD LUCK:) he answer to question 3 on its sheet. The first two questions have extra sheets for you to write your answers on them. Any part of your answers written on the wrong sheet will not be graded. A sheet of paper has two sides, you can write on both of them. e There are 3 problems in total. Some questions have several parts to them. Make sure that you attempt them all. e This is a closed book exam and no calculators are allowed. Name : ID#: Section : g 4 Q2 Q3 TOTAL ~~ Problem 1 (13 points each) Solve the following IVPs: ii- Qaxev” + 2ay cos(z”) ee ‘ y(0) =0 u 2x2yev” + sin(x?) y(0) iii- 1_y 1 T = BE ; lj=- y a” gaat yQ)= 5 iv- Pi _ git A = 1 y=-ye > y(0) i) 3S ye 5S veeosu dv S$q'= 84-0 Fg a + “ a Cusinvacosy a) a QWeosv= 4 Sov ~Veinv ' La FVEiany 4 gy, RRNA et 7 \4 , aye A Wyske fewnes - . isl oO J a = \ ee +2 arc) coscae? } . = y oP 5 Ay \ de ye® + sncQ2 ) ely ADDITIONAL SHEET FOR PROBLEM 1 ANSWER, LA Me Scte, ty) e = \ dv Ny Cosy Ay a 5. 2 sint -) ee Swn2- Sin ST \n oc a ein te \nx +) Problem 2 (19 points each) Solve the following IVPs: yl" — By" +2! =4r ; y(0)=0 , ¥(0)=3, , y"O)=4 ii- wy! ay sare =; y(1)=0 , (1) =3e a oa Ve. % mM?-3m .AaMsH sayeaye M Cm-lm-™+ 2) 20 Mm Cmom-2)-cm-2) )r0 Mm Cm-1IEN-2929 wn=o ma) Wa . oo io es =e 12 poe a 2x wot G+ E74 Ge . =| 4 Pt Adesh HK eSer Ace* 4 Boe a Y'P2 Ae 4 O- 60 *4AarrIH7AF+tO0 OGAax-6A xIB-Ar+O a A~U4 1&8 -68-0 Az=\ 98 = 661) ®-3 = pes 3 he ohana as <A = Cy ¥eje Cre eat eB prog * Oy =o AH CVeP 4 ACze? 4900) Oy _pt cp, *2~G2zO wt - 3 & + -2Cg (2) » 417+ %Me + MCg EF 4d —— 2=24 43 <4 “2Cg4a4cg ADDITIONAL SHEET FOR PROBLEM 2 ANSWER a Ss oh, =H z-ate™ as 2 are a Ax a2 2. re +x a Garza, 1S gts” = ; Sa BP axe] - Vi 2a 27eF J §q= $4 -§§ w 2.5 ~ res A ot. ah oe Sc S\ 2x € = Uxrte -§2192e Ss eee ae S21 4%4ack= WaxreX-F§ 24% eae Problem 3 (10 points) Assume g(y) is a differentiable function with a continuous derivative. Consider the following two equations: y(z) + 9(y(x)) = [alata 0 Suppose yi(a) and yo(x) are two functions such that y; satisfies the first equation, ye satisfies the SL = i —s &, | second one and moreover y;(0) = y2(0) = 0. Which of the following is true: y1 (x) > ye(z) or yo(z) 2 yi (2)?