MATH 202 Final, Summer 2016

Math 202 Dr. iH. Yamani Final Exam Summer 2016 Problem 1 (answer on pages 1,2 of the booklet) (10 pts) Find the Seneral solution of the ODE: 2, Problem 2 (answer on Pages 3,4 the Find the general solution of the ODE: ad xe as = ua ty se +] Che | x y Problem 3 (answer on Page 5 of the booklet) (10 pts) Use Laplace transforms to solve the following: y' + y= ult—1)+ 8-1) ¥(0)=0 y'(0)=0 Problem 4 (answer on Page 6 of the booklet (10 pts) Solve the following integral equation t y'=1-1- i) y(rkte (0) =0 booklet) (10 pts) 0 Problem 5 (answer on pages 7, 8 of the booklet) (10 pts each) Find the general solution of the following systems. 3 al As a X= XxX bee XxX 9 ~3 5 -4 Problem 6 (answer on page 9 of the booklet) (10 pts) Use Green’s theorem to find the counterclockwise circulation and outward flux of the field F = (= + e"siny’) i+ (« + e" cosy) j around and across r+ = 2(1+cos Q). Problem 7 (answer on pages 10 ,11 of the booklet) (10 pts) Show that the differential form in the following integral is exact, then evaluate the integral (1,0,7 ; I 2xcosz—X ) dx +(z-2y) dy+(y-x sinz) dz 3,-2,0 ae 8 (answer on pages 12, 13 of the booklet) (10 pts) Use Stokes’ theorem to evaluate the counterclockwise circulation of the field se F 27 yi t+ Bb k around the boundary C which is the intersection of the =f 2 2 plane 2x + 6y —3z =6 andthecylinderx +y =1 10 pts) on pages 14, 15 of the booklet) ( Be cic cence ticorem to find the outward flux of the field sy ee ue dary of the region which is the surface of the fi ; + zk across the boundary F=x/+ytzZ 2 2, 2 i < by the plane z=3 d spheteail sale Onby, t from the soli upper cap cu